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STATISTICAL ANALYSIS OF RADIATION DOSE 
DERIVED FROM INGESTION OF FOODS 



By 

WARD L. DOUGHERTY 



A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT 

OF THE REQUIREMENTS FOR THE DEGREE OF 

DOCTOR OF PHILOSOPHY 

UNIVERSITY OF FLORIDA 

2001 



Copyright 2001 

by 

Ward L. Dougherty 



Dedicated to 
Gwen, Justin and Michelle 

The Best Family in the World! 



ACKNOWLEDGMENTS 

I would first and foremost like to thank my wife, Gwendolyn, whose constant 
encouragement and support provided the impetus as well as the confidence to finish when 
it seemed a daunting task. My best daughter in the world, Michelle, and best son in the 
world, Justin, gave me the time and the "I Love You, Dad" at the times I needed them the 
most. I see them growing more each day, and this task of writing a dissertation seems 
insignificant to my task in parenting. You, as my family, make me more proud than 
anything else that I have done in this life. 

I would like to offer a special thanks to Dr. W. Emmett Bolch. He provided me 
support at the times when I needed it the most and encouragement and support when it 
was hard to find. 

My professors~Dr. Anghaie, Dr. Wesley Bolch, Dr. Dalton, Dr. Properzio, and 
Dr. Lindner—have been invaluable in providing not only their time and assistance but also 
their support throughout this endeavor. 

My friends-Travis Knight, Gary Chen, Paula Johnson, Katherine Wilson, and 
Steve Boddeker— were a great help in providing suggestions as well as listening and 
offering insight to help me complete this work. 

Much of this work would not have been possible without the assistance of Jerome 
Guidry, Brian Birky, and Cindy Hewitt. Their assistance and help have been invaluable 
both in the content and the background for this work. 



IV 



TABLE OF CONTENTS 

page 

ACKNOWLEDGMENTS iv 

ABSTRACT vii 

CHAPTERS 

1 INTRODUCTION 1 

Radioactive Dose to the Public 5 

Hypothesis 5 

Goals and Objectives 6 

2 LITERATURE SEARCH 7 

Introduction 7 

Dietary Intake Data 7 

Concentration of Radionuclides in Food 10 

Dose Conversion Factors 1 1 

Statistical Considerations 12 

3 DIET MODEL 13 

Introduction 13 

Initial Model 14 

NRC Nuclear Regulatory Guide 1.109 14 

RESRAD 17 

Environmental Protection Agency 18 

United States Department of Agriculture 19 

Conclusion 21 

4 EXPERIMENTATION 25 

Introduction 25 

Initial Store Samples 25 

Grocery Store Analysis 32 

Rice Experimental Analysis 37 



Histogram Analysis 43 

Conclusion and Recommendations for Future Research 47 

5 DOSE CONVERSION FACTORS 50 

Introduction 50 

Literature Search 50 

Discussion 51 

Conclusion and Recommendations 52 

6 COMMITTED EFFECTIVE DOSE EQUIVALENT 54 

Introduction 54 

Literature Search 55 

Method 55 

Analysis of 1990 FIPR Dose Diet 57 

Grocery Store Data Analysis 63 

Overall Analysis 67 

Conclusions 72 

7 CONCLUSIONS AND RECOMMENDATIONS 75 

APPENDICES 

A DATA SHEETS 80 

B CRYSTAL BALL OUTPUT DATA '. 101 

REFERENCES 206 

BIOGRAPHICAL SKETCH 209 



VI 



Abstract of Dissertation Presented to the Graduate School 

of the University of Florida in Partial Fulfillment of the 

Requirements for the Degree of Doctor of Philosophy 

STATISTICAL ANALYSIS OF RADIATION DOSE 
DERIVED FROM INGESTION OF FOODS 

By 

Ward L. Dougherty 

May 2001 

Chairman: Emmett Bolch 

Major Department: Environmental Engineering Sciences 

This analysis undertook the task of designing and implementing a methodology to 
determine an individual's probabilistic radiation dose from ingestion of foods utilizing 
Crystal Ball. A dietary intake model was determined by comparing previous existing 
models. Two principal radionuclides were considered~Lead-210 (Pb-210) and Radium 
226 (Ra-226). Samples from three different local grocery stores-Publix, Winn Dixie, and 
Albertsons—were counted on a gamma spectroscopy system with a GeLi detector. The 
same food samples were considered as those in the original FIPR database. A statistical 
analysis, utilizing the Crystal Ball program, was performed on the data to assess the most 
accurate distribution to use for these data. This allowed a determination of a radiation 
dose to an individual based on the above information collected. 

Based on the analyses performed, radiation dose for grocery store samples was 
lower for Radium-226 than FIPR debris analyses, 2.7 vs. 5.91 mrem/yr. Lead-210 had a 



Vll 



higher dose in the grocery store sample than the FIPR debris analyses, 21.4 vs. 518 
mrem/yr. 

The output radiation dose was higher for all evaluations when an accurate 
estimation of distributions for each value was considered. Radium-226 radiation dose for 
FIPR and grocery rose to 9.56 and 4.38 mrem/yr. Radiation dose from ingestion of Pb- 
210 rose to 34.7 and 854 mrem/yr for FIPR and grocery data, respectively. 

Lead-210 was higher than initial doses for many reasons: Different peak 
examined, lower edge of detection limit, and minimum detectable concentration was 
considered. FIPR did not utilize grocery samples as a control because they calculated 
radiation dose that appeared unreasonably high. 

Consideration of distributions with the initial values allowed reevaluation of 
radiation does and showed a significant difference to original deterministic values. This 
work shows the value and importance of considering distributions to ensure that a 
person's radiation dose is accurately calculated. 

Probabilistic dose methodology was proved to be a more accurate and realistic 
method of radiation dose determination. This type of methodology provides a visual 
presentation of dose distribution that can be a vital aid in risk methodology. 



Vlll 



CHAPTER 1 
INTRODUCTION 

The purpose of this study was to design and implement a methodology utilizing 
the Crystal Ball* program to determine a statistical value, a number, and associated 
fluctuation of an individual's radiation dose based on foods bought from local stores in 
Gainesville, Florida, and to provide comparison through analysis to a similar previous 
study. 

The most straightforward approach to an individual's radiation dose 
determination has been to use a deterministic approach. The calculation stated below 
will provide a committed effective dose equivalent (CEDE) based on ingestion (intake) 
of a specific radionuclide, a certain concentration in the food and a dose conversion 
factor (DCF). 

Intake * Concentration * DCF = CEDE (Equation 1-1) 

where 

Intake = individual dietary intake (g/day or g/yr) 

Concentration = amount of radionuclide in for (pCi/g or pCi/kg) 

DCF = dose conversion factor—term to convert activity in foods ingested 
to dose (mrem/pCi). 



Crystal Ball is a statistical analyses program written by Decisioneering as an addition to Microsoft 
Excel. This provides Monte Carlo sampling of input parameter distribution and trials to determine an 
output distribution. 

1 



CEDE is a dose quantity that describes the long-term dose to an individual 
from an intake of radioactive material (Shleien, Slaback, & Birky, 1998, pp. 3-5). 
Depending on what type of dose the individual was trying to calculate, each variable in 
the calculation had essentially one, and only one, value determined and set down in the 
guidelines by various agencies. The guidelines were put into recommendations, and 
these were subsequently, though much later, written into regulatory guidelines. The 
advent of better computational methods for radiation dose determination due to better 
computer hardware and software and increased amounts of experimental data is now 
leading to more accurate determination of the described dose utilizing a probabilistic 
approach. 

The method of a probabilistic approach versus deterministic approach utilizes 
the information that the variables are each described by a statistical distribution. These 
statistical distributions are defined by a mean and its associated fluctuations. Figure 1-1 
illustrates the methodology and the concept behind this approach. This method provides 
a more accurate description of the actual range that each variable might have and the 
probability assigned to it. 



». T ». 


! dt ] 



* 




* 



tatfM 


i; 


i 




& 


1 


fc 


\ 


P>', ; J 




Intake 
Distribution 



Concentration 
Distribution 



DCF 

Distribution 



CEDE Dose 
Distribution 



Figure 1-1. Probabilistic Method of Dose Calculation 



The Health Physics Society has stated in their most recent position papers that 
risk assessment must be considered in the context of uncertainties in the estimates 
(Burk, 2000, p. 232). This statement is in light of the fact that more people and 
organizations are approaching risk-based policy. 

This approach allows determination of a final answer, in this case dose, that also 
has a distribution. This type of an answer, final dose described by a distribution, 
provides a more accurate answer by taking into account the distributions of the 
variables with their associated errors and promulgating them through the equation to 
come to a final solution. 

This document is set up as individual chapters connected by the overall 
introduction and conclusion. Each chapter has its own introduction and conclusion. 
Additionally, each chapter describes the previous and following chapters to provide a 
more unified whole to the reader. The chapters in this document and a brief description 
of each are organized as follows: 

Chapter 1 (Introduction). This chapter provides an overview of the project of 
both its scope and breadth. The types of approaches to radiation dose evaluation are 
discussed, both past and present. A brief overview of the different sections of the 
chapter is discussed. 

Chapter 2 (Literature Search). The applicable literature is cited in this chapter. 
The various studies that have been performed that are specific to the radionuclides, 
methodology, statistics, and research in this area are reviewed in this chapter. 
Additional sources are reviewed to determine current work in the area of food 
radioactivity analysis and diet models utilized to determine dose to an individual. 



Chapter 3 (Diet Model). The literary references for the individual diet is 
provided in this chapter. The methodology for determination of the amended diet is 
discussed in this chapter. The diet is described for an individual in this portion of the 
paper. A determination of an individual's intake is made in this chapter as well as the 
rationale behind the decision. 

Chapter 4 (Experimentation). Description of the samples bought, prepared, and 
counted from three different local stores is considered in this chapter. Concentration 
data for various foods is determined from the experimental data collected. The 
distribution of the concentration of radionuclides in food is also undertaken and 
resolved in this chapter with the analysis of an additional set of samples. 

Chapter 5 (Dose Conversion Factors). Explanation of the Environmental 
Protection Agency's Dose Conversion Factors (DCFs) is provided. The discussion of 
the various dose conversion factors is considered, and assignment is made to a statistical 
distribution to the dose conversion factor variable. 

Chapter 6 (Committed Effective Dose Equivalent-CEDE) . Analysis of the 
previous chapters with regard to the calculation of the CEDE is considered utilizing 
Crystal Ball's statistical analysis tools to configure the variables and determine the 
output. The various methodologies and analyses on both the original 1990 data and the 
newly measured grocery store data are presented to determine the final dose and the 
final dose distributions that accompany these data. 

Chapter 7 (Results, Conclusions, and Recommendations). The analysis of the 
final dose determinations and the program to achieve them are presented. 



Recommendations for future work are presented, and conclusions based on the output 
from the above chapters are provided. 

Radiation Dose to the Public 
An individual is expected to get an average annual dose of 360 mrem (Shleien 
1998). Geographic and other factors can change this value from 75 to 5000 mrem. 
Individuals are constantly exposed to radiation of all types: cosmic, terrestrial, natural 
internal. Without sunlight life itself would be impossible, but radiation has a bad 
connotation to the public. People fear the word and the associated images that it 
conjures up. The public thinks of Three Mile Island and Chernyobl when the issue is 
discussed, but radiation is all around us and is a vital and important part of our world. 
The plants are the focus of this paper. This dissertation and chapter seek to determine 
through theory and experimentation what level of radioactivity is found in our food and 
provide a statistical analysis for an improved completeness of description. 

Hypothesis 
The hypothesis of this dissertation is that the ingestion of radioactivity found in 
of foods bought from local stores should be measured and analyzed to determine its 
significance. This value that is experimentally measured from foods should have a 
statistical value that can be described by a distribution. The final dose that is determined 
from these measured values additionally should have a statistical value with a 
distribution. 



Goals and Objectives 
The following provides a list of goals and objectives for this dissertation: 

1 . Perform a literature search on radioactivity of foods bought in local stores in 
Gainesville, Florida, as well as previous studies performed on Florida foods 
or the associated radionuclides. 

2. Determine a dietary intake of foods based on previous studies. 

3. Measure foods bought from three different local stores and determine 
radioactivity of lead-210 and radium-226 in these samples. 

4. Measure one set of samples to determine distribution to be associated with 
concentration of radionuclides in food. 

5. Determine the distribution to utilize for the EPA's Dose Conversion Factor. 

6. Perform Crystal Ball analysis to determine the final dose, in distribution 
form, to the individual from the original FIPR study data and from the 
experimentally measured grocery store data. 

7. Analyze the results to provide a comparison to the total dose. 

8. Compare deterministic and probabilistic methodology of dose calculation. 



CHAPTER 2 
LITERATURE SEARCH 



Introduction 
This dissertation covers several fields of study; therefore, a literature search 
needs to be performed to find the relevant references in each of these areas. The areas of 
search that are involved in this dissertation are dietary intake, food concentration, 
radionuclide, dose conversion factors, committed effective dose equivalent, and 
statistical distributions. This literature search examines the various literature sources 
that were utilized for each of these categories. 

Dietary Intake Data 

The dietary intake of an individual is quite often information that is specific to 
the individual. The dietary intake varies by person due to individuality of the person as 
well as local customs and availability of food. In an effort to determine dietary intake of 
an individual in Florida, the first source that was researched included previous studies 
performed in Florida. 

A study of radioactivity in Florida foods and the diet of Floridians necessarily 
begins with an assessment of study in the field, both past and present. Some of the most 
recent work in Florida that has examined radioactivity in foods in Florida was 
performed by the Florida Institute of Phosphate Research (FIPR) (Guidry, Roessler, 
Bolch, McClave, Hewitt, & Abel, 1990). This organization was created by the Florida 
Legislature in 1978 to conduct supportive research to the development of the state's 



phosphate resources. This organization has done studies in this field due to its interest in 
the environmental aspect of phosphate mining. 

There are three sources that provided information both for the dietary model and 
the initial concentration of radionuclides in food grown on phosphate and related lands. 
The first document is the 1986 FIPR report that provided the initial analysis of radium- 
226, lead-210, and polonium-210 in foods grown on phosphate lands (Guidry, Bolch, 
Roessler, McClave, & Moon, 1986). The initial diet model that describes dietary intake 
was first presented in this document. The method of analysis and the dose evaluation 
were described in this book. Simplified analysis of radionuclide concentration in foods 
was performed to determine dose to an individual. Three individuals were considered: 
control, local, and maximum. A control individual was a reference individual who 
consumes "sampled" foods not from mining-related lands. A local individual consumed 
10 percent of his "sampled" foods from phosphate lands and 90 percent from control 
lands. A maximum individual consumed 100 percent of "sampled" foods in his diet 
from phosphate (clay) lands. This individual reflects worst case scenario (Guidry et al., 
1990, pp. 118-119). 

The next two documents were associated with this initial document. Brian 
Birky's master's thesis referred to the previous document and used the same 
methodology, diet, and radionuclides to determine dose attributable to technological 
enhancement of this phosphate reclaimed land (Birky, 1990). This document detailed 
the previous methods and studies that were utilized to prepare, enclose, and measure the 
experimental samples. This thesis discussed the methodology utilized to calculate the 



dose to an individual directly from the dietary intake spreadsheet. This thesis was much 
more descriptive in the details of diet and dose calculation than the initial paper. 

The 1990 FIPR paper was a continuing study based on the recommendations of 
the 1986 FIPR paper mentioned above (Guidry et al., 1990). This paper utilized the 
same basic dietary intake model of the initial study. Some of the same radionuclides 
were considered. This document focused primarily on three radionuclides and five land 
types. Three types of individuals were considered in this paper also: local, control, and 
maximum. The basic dietary model, with few revisions, was presented in this paper. 
This paper analyzed the differences in the data as well as performing regression analysis 
on the collected data. This paper had more data points added and more analysis 
performed that detailed the soil-to-plant transfer model and refined the dietary intake 
model. 

FIPR has continued to improve its database with more samples since this report, 
and the extended database will be available in a publication in the near future. The 
current research and work also has continued to smooth the statistical data. 

An important point was brought about by direct discussion with Dr. Birky: 
sampled versus nonsampled diets (B. Birky, personal communication, March 13, 2001). 
A vital consideration in any analysis is the thought given to what foods were and were 
not sampled and how to consider them in the final dose determination. These papers and 
the subsequent meeting provided invaluable insight into this particular point. 

These papers primarily discuss the various analyses performed on foods grown 
on Florida lands in general and phosphate lands in Florida in particular. These were the 
most useful and pertinent with regard to this analysis. 



10 

Concentration of Radionuclides in Food 

The concentration of radionuclides in food has been studied in several areas and 
contexts. The previous three papers discussed this very subject and determined the 
concentration of several radionuclides in various foods grown on phosphate-related 
lands. 

A study funded by FIPR and performed by the Audubon Society studied the 
concentration of radium-226 in alligators, armadillos, and soft and hard shell turtles 
(Pritchard & Bloodwell, 1986). These data relate that the hazard from eating these 
mammals on mine-impacted lands is unclear. 

Dietary intake of lead-210 has been discussed in several articles. Linsalata 
(1994) discusses human exposures along plant and animal pathways to thorium, 
uranium, radium, lead, and polonium. The exposure pathways were considered, and the 
author states that much more work needs to be done in assessing the transfer of lead- 
210 and polonium-210 in the human food chain. 

Morse and Welford (1971) discusses the dietary intake of lead-210 in the diet of 
New York city residents with a result of 1.2 pCi lead-210 per day. This food diet only 
included 19 food items. An interesting note is the fact that the concentration of lead-210 
was calculated as 0.70 pCi lead-210/kg food. 

An analysis was performed on radionuclide contact in Hong Kong food. Yu and 
Mao (1999) gives an excellent description of the types of gamma spectroscopy system 
used. The diet model and the results were detailed in tabular form with seven 
radionuclides under examination. Potassium-40 was found in all solid food and drink 



11 

samples. Lead-210 was measured as being greater than half the contribution to the dose 
from natural radioactivity. 

Carvalho (1995) analyzed the Portuguese population for intake of polonium-210 
and lead-210. The author primarily examined these two radionuclides and their 
ingestion rates for the population. This paper supports the postulation of a different diet 
model for a different population. The point is also made in this paper that cooking the 
various food prior to eating is not taken into account. 

Dose Conversion Factors 

The data for the dose conversion factor (DCF) came from four sources. The first 
source was Federal Regulatory Guide No. 1 1 (EPA, 1988, pp. 155-179). This document 
provides the methodology used to calculate the DCFs for inhalation, submersion and 
ingestion. The tables of the various DCF data for various radionuclides is included in 
this manual. 

The next two articles, International Council on Radiation Protection (ICRP) 68 
(ICRP, 1994) and 72 (ICRP, 1996), provide age-dependent DCFs for workers and 
members of the public from intake of radionuclides. Although they were examined for 
the purposes of this report, the new DCFs were not utilized for the purposes of 
consistency. 

The fourth reference for these data was a solution manual that calculated a dose 
conversion factor for strontium-90 (Turner, Bogard, Hunt, & Rhea, 1988). This was 
utilized as a reference to describe the method to obtain a dose per unit intake factor 
from the initial data. 



12 

Statistical Considerations 

Statistics play a major role in the analyses of this study. Information to utilize 
Crystal Ball comes from the manual provided with the program (Decisioneering, 1996). 
The manual provides the instruction to utilize the program as well as examples to 
familiarize the novice with the operation of the various tools built into the software. 

These sources provided the nucleus of the reference material researched to 
obtain the necessary data for the background to perform this research and analysis. The 
following chapter discusses the diet model and how it was determined. The next chapter 
discusses the dose conversion factor to determine which dose conversion factor to use 
and what distribution to assign to this value for an accurate estimate of dose 
distribution. 



CHAPTER 3 
DIET MODEL 



Introduction 

This chapter is a literature search and subsequent analysis of various diet models 
currently utilized by regulatory agencies and other organizations. The object of this 
portion of the work is to determine the most accurate diet model for calculating radiation 
dose to individuals in Florida from their dietary intake. 

The choice of a proper diet model is vital to determine dose to an individual from 
ingestion. Diet model is not as accurate a term as dietary intake model. This distinction 
may seem small, but it is significant. A diet model refers to the assumed or predicted 
intake of certain sources of food to individuals. Conversely, a dietary intake model 
utilizes surveys of the public to ascertain actual food intake. The goal of this chapter is to 
ascertain, using major and well-established sources, the most accurate and comprehensive 
source for the dietary intake model for use with our dose evaluation model. 

Numerous sources were researched to obtain this goal. The major sources 
researched were the Pennington Model, Nuclear Regulatory Commission, the United 
States Department of Agriculture CHFSII 1976-1978 Study, the 1994-1996 NFCS study, 
RESRAD, and the Environmental Protection Agency. All of these were studied to 
determine the most suitable diet model for use with a program to determine dose to the 
individual. 



13 



14 

Several factors are considered in an effort to determine the right dietary intake 
source for our program and dose determination program. The factors that will be 
considered to decide on the right source for the final dietary intake model will be the 
following: the date of the publication, the sources of the publication, the comprehensive 
quality of the data, and the compatibility with the previous FIPR model. 

Initial Model 

The diet model used to calculate radiation dose in the 1986 and 1990 FIPR studies 
was the 1983 Pennington dietary intake model (Pennington, 1983). The Pennington diet 
model was derived from the Food and Drug Administration's Total Diet Study. The most 
recent revision of this study was based on data from the 1987-88 National Food 
Consumption Survey (Pennington, 1992). This information was discussed in the 1990 
FIPR study dealing with radioactivity of foods grown on phosphate lands (Guidry et al., 
1990). The dietary intake model used only the adult male category and regrouped the 201 
items in the Pennington diet intake model. Table 3-1 shows the data from that paper. 

As can be seen from this table, there are 17 major categories and 43 
subcategories. It detailed intake in grams per day. The sources that are being studied need 
to be examined to determine unit compatibility and possibility of improvement over this 
initial model. 

NRC Nuclear Regulatory Guide 1.109 
The first alternate source examined was the Nuclear Regulatory Commission. The 
mission of the U.S. Nuclear Regulatory Commission (NRC) is to ensure adequate 
protection of the public health and safety, the common defense and security, and the 



Table 3-1: Diet Food Items from Pennington Diet (Guidry et al., 1990) 



15 



Source 


Intake 


Item 


(g/day) 






DAIRY 




Milk 


280.99 


Cheese 


22.41 


MEAT 




Beef 


129.27 


Pork 


39.54 


Other 


69 


FISH 


20.06 


EGGS 


30.95 


CEREAL FOOD 




Corn Grain 


5.18 


Grain 


4.55 


Cereals/Bread 


174.7 


CAULIFLOWER/BROCCOLI 




Cauliflower 


0.71 


Broccoli 


2.8 


LEAFY/COLE VEGETABLE 




Cabbage 


7.04 


Collard Greens 


0.45 


Lettuce 


23.38 


Mustard Greens 


0.45 


Spinach 


3.28 


Turnip Greens 


0.45 


Other 


0.76 


Celery 


0.62 


LEGUMES 




Green Peas 


7.29 


Other Beans 


25.71 


Nuts 


4.94 


Other 


11.28 



Source 


Intake 


Item 


(g/day) 






SEEDS/GRAINS 




B lackeyed Peas 


5.61 


Rice 


22.94 


Yellow Corn 


14.41 


TUBERS/ROOTS 




Carrots 


2.92 


Onion 


4.19 


Radish 


0.32 


Turnip 


0.42 


Potatoes 


85.22 


Other 


1.1 


GARDEN FRUIT 




Cucumbers 


2.62 


Greens Beans 


8.8 


Green Peppers 


1.99 


Strawberries 


1.23 


Tomato 


25.18 


Watermelon 


3.44 


Yellow Squash/Zucchini 


1.26 


Other 


6.55 


TREE FRUIT 




Citrus 




Orange 


85.26 


Grapefruit 


7.78 


Lemon 


10.71 


Other 


60.36 


SOUPS 


36.82 


CONDIMENTS 


54.12 


DESSERTS 


78.3 


BEVERAGE 


1172.44 


WATER 


512 


TOTAL 


3071.8 



16 

environment in the use of nuclear materials in the United States (NRC, 2000). This board 
and its associated bureaucracy accomplish this mission by presiding over the various 
aspects of reactor operation, siting, and licensing. Numerous programs and regulations 
are employed to determine the safety and feasibility of siting and operating a plant. NRC 
Regulatory Guide 1.109, Calculation of Annual Doses to Man from Routine Releases of 
Reactor Effluents for the Purpose of Evaluating Compliance with 10 CFR Part 50, 
Appendix I, employs a dietary intake model to determine dose to an individual from 
ingestion of radionuclides (NRC, 1977). Tables 3-2 and 3-3 list the consumption of 
various foods such as fruits, vegetables, meat, and milk. 

This information is listed for various groups of people: child, teen, and adult. 
Additionally, each table details the intake for the average individual and the maximum 
individual. The data in these tables come from ICRP Pub # 23 from 1975 (NRC, 1977) 
and AER USDA report of 1974 (NRC, 1977). There are only six categories displayed in 
Table 3-2 and seven categories in Table 3-3. The data are limited when compared to the 
Pennington dietary intake model. The units are compatible when converted. 



Table 3-2: NRC NRG 1.109 Average Individual Intake (NRC, 1977) 



Source 


Child 


Teenage 


Adult 










Fruits, Veg and Grains (kg/yr) 


200 


240 


190 


Milk (L/yr) 


170 


200 


110 


Meat and Poultry (kg/yr) 


37 


59 


95 


Fish (kg/yr) 


2.2 


5.2 


6.9 


Seafood (kg/yr) 


0.33 


0.75 


1 


Drinking Water (L/yr) 


260 


260 


360 



17 



Table 3-3: NRC NRG 1.109 Maximum Individual Intake (NRC, 1977) 



Source 


Child 


Teenage 


Adult 










Fruits, Veg and Grains (kg/yr) 


520 


630 


520 


Leafy Veg (kg/yr) 


26 


42 


64 


Milk (L/yr) 


330 


400 


310 


Meat and Poultry (kg/yr) 


41 


65 


110 


Fish (kg/yr) 


6.9 


16 


21 


Seafood (kg/yr) 


1.7 


3.8 


5 


Other Seafood (kg/yr) 


1.7 


3.8 


5 


Drinking Water (L/yr) 


510 


510 


730 



RESRAD 
RESRAD was researched next. This program was designed by the Environmental 
Assessment Division of Argonne National laboratories. It was approved by the 
Department of Energy for evaluation of radioactively contaminated sites (ANL, 1989). 
This code has undergone several benchmarking analyses. The first release of the code 
was in 1989. It allows either user input of numerous variables or default variables. Table 
3-4 shows these data in tabular form. As can be seen from this table, there are only five 
food groups in this diet. 



Table 3-4: RESRAD Dietary Intake Parameters (ANL, 1989) 



Source 


Default 


Units 


Min 


Max 












Fish 


5.4 


kg/yr 





1000 


Other seafood 


0.9 


kg/yr 





100 


Fruit, Veg and Grain 


160 


kg/yr 





1000 


Leafy Vegetable 


14 


kg/yr 





100 


Meat and Poultry 


63 


kg/yr 





300 



18 

There are various sources for this chapter. The seafood data come from the EPA 
recommendation of two reports performed in 1981 and 1982. The data for the fruit, 
vegetable, and grain come from the EPA 1990 paper which was derived from two earlier 
documents: Foods Commonly Eaten by Individuals: Amount Per Day and Per Eating 
Occasion and Food Consumption: Households in the United States, Seasons and Year 
1977-1978. Additionally, since the 1990 document did not address grain consumption, 
these data were taken from the NuReg 1 . 1 09 discussed above. For the leafy vegetable 
consumption rate, the code refers back to NuReg 1 . 1 09 and the average individual. The 
meat and poultry consumption rate is also determined from NuReg 1.109 and the EPA's 
1990 paper with comparison to another paper by Gilbert et al. from 1983. This database, 
like the NRC model, has a limited number of data points. The units are compatible, but 
due to the data point limitation, it is not considered as feasible for our diet intake model 
(ANL, 1989). 

Environmental Protection Agency 
The Environmental Protection Agency (EPA) has numerous documents, as is 
evidenced by the above discussion of RESRAD information sources. The most 
applicable of them is The Exposure Factors Handbook (EPA, 1997). This was first 
published in 1989 with its update published in 1997. This paper has a wealth of 
information about food consumption by area, age, sex, and various foods; however, this 
information is far too voluminous to include in this chapter. The key study utilized to 
perform this analysis was the EPA analysis of 1989-1991 USD A CSFII study (USD A, 
1996). It should be noted here that this analysis in the exposure factor handbook also 



19 

included mean and standard errors that might be useful in statistical analyses performed 
as an extension of this work by future researchers. 

The EPA's Federal Guidance Report # 13 : Cancer Risk Coefficients for 
Environmental Exposure to Radionuclides (EPA, 1995) was also researched but was not 
seriously considered due to the fact that the intake considered is not broken down by food 
groups, and the units are in kcal/day, units that are not compatible with our comparison. 
The limited number of data points also make it incompatible with the previous study. 

United States Department of Agriculture 
The United States Department of Agriculture (USDA) conducts several food 
consumption surveys at regular intervals. One of these was mentioned as a reference in 
the EPA Exposure Factors Handbook (EPA, 1997). Numerous articles discuss the various 
surveys performed by the USDA (Borrud, Enns, & Mickle, 1996) as well as the trends in 
food and nutrient intake that are derived from them (Enns, Goldman, & Cook, 1997). 
This last referenced article compares the 1977 NFCS, the 1991 CSFII, and the 1995 
CSFII. There are two major USDA food intake survey projects. They are the Nationwide 
Food Consumption Survey (NFCS) and the Continuing Survey of Food Intake by 
individuals (CFSII). The NFCS is conducted approximately every 10 years with the most 
recent performed in 1987-1988. It should be noted here that the original food intake 
model in the 1990 FIPR report came from the Pennington model. This model was derived 
from two other studies, one of which was the NFCS study. 

The most recent CFSII was conducted in 1994 -1996. Over the course of the 
three-year study over 16,000 individuals were queried about their dietary intake on two 
nonconsecutive days. Obviously, this study produced a large amount of data. These data 



20 

were separated in much the same way as the EPA data discussed above. This study has 
more data points than that of the EPA, NRC or RESRAD studies, but it only has 
essentially 1 1 major food categories and 15 subcategories. Table 3-5 shows these data for 
a one-day sampling of male respondents. 



Table 3-5: 1994-1996 CFSII Dietary Intake Data 



Source 


Intake 


Item 


(gm/day) 






Total Grain Products 


361 


Yeast Breads and Rolls 


63 


Cereals and Pasta 


89 


Ready to Eat Cereal 


16 


Mixtures mainly grain 


128 


Total Vegetables 


242 


Dark Green Vegetables 


14 


Deep Yellow Vegetables 


8 


Tomatoes 


37 


Total Fruits 


172 


Citrus Fruits 


65 


Bananas 


19 


Non Citrus juices and nectars 


19 


Total Mlk and milk products 


256 


Total fluid milk 


178 


Whole milk 


54 


Lowfat milk 


85 


Skim milk 


35 


Milk Desserts 


33 


Cheese 


18 


Total meat, Poultry and Fish 


275 


Beef 


38 


Pork 


15 


Mixtures mainly meat, poulty and Fish 


137 


Eggs 


23 


Legumes 


31 


Nuts and Seeds 


4 



21 

The source of these data, although statistically more accurate in that it came 
straight from a survey of a large number of respondents, should also be suspect for the 
simple reason that it is a survey. Surveys have their own inaccuracies due to the people 
questioned and the method of questioning. 

Conclusion 

The above databases show that there are a limited number of choices for a 
comprehensive source for our diet model. The most promising beside the original diet 
model, the Pennington dietary intake model, is the USDA 1994-1996 CFSII database. 
This has the largest number of food groups compared to the other databases. The units, 
grams per year, are the same as the initial diet model. The Pennington model source was 
from the United States Department of Agriculture NCF study. This database comes from 
the same organization and the database is newer with more respondents surveyed. These 
reasons provide that the final source for the dose estimate program should be either the 
original Pennington Model or the diet from the USDA CFSII 1994-1996. A newer 
version of the Pennington model would be ideal, but foregoing this possibility the author 
chooses to utilize the existing Pennington model minimally updated with data from the 
CFSII 1994-1996 survey. These data are shown in Table 3-6. Should a newer more 
complete version of the Pennington model become available another comparison will be 
performed to determine the most suitable model. 

Table 3-7 shows the various factors considered in a decision matrix to allow 
determination of a dietary intake model. Five factors were important considerations. The 
most important factor was the possibility of similar studies being performed. The initial 
Pennington model had the dose calculation performed in 1990. The date of publication 



22 



was the next factor. Two models had more recent publication dates but due to the 
following three factors were unsuitable. 



Table 3-6: Dietary Model Intake 



Source 


Intake 


Item 


(g./day) 






DAIRY 




Milk 


193 


Cheese 


18 


MEAT 




Beef 


37 


Pork 


15 


Other 


217 


FISH 


14 


EGGS 


24 


CEREAL FOOD 




Corn Grain 


5.18 


Grain 


4.55 


Cereals/Bread 


174.7 


CAULIFLOWER/BROCCOLI 




Cauliflower 


0.71 


Broccoli 


2.8 


LEAFY/COLE VEGETABLE 




Cabbage 


7.04 


Collard Greens 


0.45 


Lettuce 


23.38 


Mustard Greens 


0.45 


Spinach 


3.28 


Turnip Greens 


0.45 


Other 


0.76 


Celery 


0.62 


LEGUMES 




Green Peas 


7.29 


Other Beans 


25.71 


Nuts 


4.94 


Other 


11.28 



Source 


Intake 


Item 


(g./day) 






SEEDS/GRAINS 




Blackeyed Peas 


5.61 


Rice 


22.94 


Yellow Corn 


14.41 


TUBERS/ROOTS 




Carrots 


2.92 


Onion 


4.19 


Radish 


0.32 


Turnip 


0.42 


Potatoes 


85.22 


Other 


1.1 


GARDEN FRUIT 




Cucumbers 


2.62 


Greens Beans 


8.8 


Green Peppers 


1.99 


Strawberries 


1.23 


Tomato 


25.18 


Watermelon 


3.44 


Yellow Squash/Zucchini 


1.26 


Other 


6.55 


TREE FRUIT 




Citrus 




Orange 


85.26 


Grapefruit 


7.78 


Lemon 


10.71 


Other 


60.36 


SOUPS 


36.82 


CONDIMENTS 


54.12 


DESSERTS 


78.3 


BEVERAGE 


1172.44 


WATER 


512 


TOTAL 


2997.58 



23 



Table 3-7: Decision Matrix Table 



Model 


Similar 
Studies 


Date of 
Publication 


Source 


Quality 


Comparability 


Pennington 1990 


Yes 


1990 


1987/8 


17 and 43 


Good 


NRC NRG 1.109 


No 


1977 


1974 


5 or 7 


Fair 


RESRAD 


No 


1989 


1977 


5 


Fair 


EPA-EFH 


No 


1997 


1989/91 


— 


Poor 


EPAFRG#13 


No 


1995 


1974 


— 


Not 



The source of each model was examined as the third factor. The EPA Exposure 
Factor Handbook had the most recent source with the Pennington model second. 
Quantity, or number of food categories for overall diet and possibility to analyze them, 
was considered with Pennington having the most complete diet and most available food 
categories. Both EPA documents in this category were not applicable due to the large 
number of categories and dietary items. Comparability was considered as the fifth and 
lowest priority category. This column relates to the format in which the data are 
presented and similarity of individual studies. As an example, EPA's FGR #13 is in Kcal 
per day, which is difficult to compare with grams or kilograms per day. The Pennington 
had good comparability, whiel NRC 1.109 resrad were listed as fair due to having 
comparable units without a specified individual such as a 25-year-old male. All of this 
led the author to a determination of an updated Pennington diet model as the best choice 
for the dietary intake model. 

A dietary intake model choice is made more difficult due to the fact that it is hard, 
if not impossible, to define a "normal" individual or diet. This is even more complicated 
when a limited area such as Florida or Gainesville is chosen. The closest similar previous 
study to determine individual doses in Florida was the Pennington model. Therefore, an 
updated Pennington model was chosen. 



24 

The errors associated with the various diets were not included only the EPA EFH 
had errors associated with the dietary intake. The analyses performed in the following 
chapters assign various distributions which include fluctuations, errors, and variability. 

The distribution for this factor is assumed to be a lognormal due to the facts that 
dietary intake is a variable in which the individual has a wide latitude of intake and 
therefore some will exercise this power. Allowing for this fact, the factor was evaluated 
as a lognormal distribution as well as a normal (gaussian) distribution. 

The next chapter discusses the results derived from the gamma spectroscopy 
analysis of the local samples bought and analyzed from the various stores in the 
Gainesville, Florida, area. 



CHAPTER 4 
EXPERIMENTATION 



Introduction 



This is the fourth in a series of seven chapters the overall goal of which is to 
design and implement a methodology utilizing the Crystal Ball program to determine a 
statistical value, a number, and associated fluctuation of an individual's radiation dose 
based on foods bought from local stores in Gainesville, Florida, and to provide 
comparison through analysis to a similar previous study. This dose will be described not 
by a singular number but will be expressed as a distribution. This distribution will be 
determined by a series of analyses, on both the 1990 FIPR diet and a new set of data 
determined by experimentation utilizing the Crystal Ball program to evaluate the 
distribution and value of the final dose. 

Crystal Ball is a forecasting program that is an "add-on" program to Microsoft 
Excel (Decisioneering, 1996). Initially designed as a financial forecasting program for 
business analysts, this program has a unique and powerful ability to determine the dose 
distributions that are under investigation. A Monte Carlo random sampling technique is 
utilized within the program to determine the distribution of the final outcome. 

The goal of this chapter is to describe the analysis performed on various samples 
to determine the concentration and distribution of radionuclides in the foods purchased. 
This goal will be accomplished in several stages. Previous work and literature search was 
undertaken to determine what to measure, how to measure it, and what foods to analyze. 

25 



26 

Next, a discussion of the various radionuclides under consideration will be reviewed. 
Then, the actual experimental analyses will be described. Four separate analyses were 
performed to measure the concentration of radionuclide concentration in food. The four 
analyses will be described along with the information obtained. The conclusion will 
consolidate all the data 

Initial Store Samples 
Literature Search 

The literature search described in the second chapter of this series described the 
previous samples taken from various locations to assess the radionuclide concentrations 
in foods grown in several regions around the world. The focus of this chapter was 
necessarily limited to a study of radionuclide concentration of foods in Florida. The 
additional sources of literature provided useful comparisons on the various radionuclides 
considered, the diets studied, and the methods of analyses. 

There are three sources that provided information both for the dietary model and 
the initial concentration of radionuclides in food grown on phosphate and related lands. 
The first document is the 1986 FIPR report that provided the initial analysis of radium- 
226, lead-210, and polonium-210 in foods grown on phosphate lands (Guidry et al., 
1986). Other radionuclides were also examined in these data. The diet model that 
describes dietary intake was first presented in this document. The method of analysis and 
the dose evaluation were described in this book. Simplified analysis of radionuclide 
concentration in foods was performed to determine dose to an individual. Three types of 
individuals were considered: control, local, and maximum. 



27 

The next two documents were associated with this initial document. Brian Birky's 
master's thesis referred to the previous document and used the same methodology, diet, 
and radionuclides to determine dose attributable to technological enhancement of this 
phosphate-reclaimed land (Birky, 1990). Birky (1990) detailed the previous methods and 
studies that were utilized to prepare, enclose, and measure the experimental samples. 

Additionally, the methodology utilized to calculate the dose to an individual 
directly from the dietary intake spreadsheet was explained. The explanation was much 
more descriptive in the details of diet and dose calculation than the initial chapter. 

Guidry et al. (1990) conducted a continuing study based on the recommendations 
of the 1986 FIPR paper. The same basic dietary intake model was used as that considered 
in Guidry et al. (1986). The same radionuclides were considered. Three radionuclides and 
five land types were examined. Three types of individuals were considered in this paper 
also: local, control, and maximum. The basic dietary model, with few revisions, was 
presented in this paper. The differences in the data were analyzed. Regression analysis 
was performed on the collected data. More data points were added from the previous 
study, and more analyses were performed that detailed the soil to plant transfer model 
and refined the dietary intake model. 

FIPR has continued to improve its database with more samples since this report, 
and the extended database will be available in a publication in the near future. The 
current research and work also has continued to smooth the statistical data. These 
chapters primarily discuss the various analyses performed on foods grown on Florida 
lands in general and phosphate lands in Florida in particular and are the most useful and 
pertinent to this study. 



28 

The concentration of radionuclides in food has been studied in several areas and 
contexts. The previous three chapters discussed this very subject and determined the 
concentration of several radionuclides in various foods grown on phosphate-related lands. 

To provide for data for this report, and as a means of comparison for the previous 
report, similar samples were taken from local stores. This chapter will discuss the 
radionuclide considerations, the stores utilized, the samples taken, the method of 
measurement, and the results of the measurements. 

Radionuclide Considerations 

Three radionuclides were considered consistently in the previous reports: lead- 
210, radium-226, and polonium-210. Each of these is of concern for various reasons. All 
are from the uranium decay chain, and two are progeny of radium-226. The lead-210 and 
radium-226 radionuclides will be discussed in turn. 
Lead-210 (Pb-2 10) 

This radionuclide is a progeny of radium-226 through decay of radon-222. Lead-210, 
unlike radon, is a reactive radioisotope that adsorb onto particulates and therefore pose a 
possible risk to humans through ingestion and inhalation. Most environmental lead is 
associated with sediments, and the rest is in dissolved form. Short-term exposure to even 
low levels can cause changes in red blood cell chemistry; developmental problems; and 
attention span, hearing and hearing and learning disabilities in children. Adult short-term 
exposure can cause a slight increase in blood pressure. Long-term exposure has been 
linked to cerebrovascular and kidney disease (Weiner, 2000, pp. 221, 222). 
Environmental and toxic considerations aside, a large fraction of the lead-210 in the 
environment have been formed following the decay of radon-222. Therefore, higher 



29 

concentrations of lead-210 are found in the surface soils. This increases the chance of 
intake through the human food chain adding to an individual's dose (Harley, 1988). 
Additionally, lead was analyzed in the previous FIPR studies and provides a point of 
comparison for the experimental data obtained in this study. 
Radium-226 fRa-226) 

There are more data on this radionuclide than on any other radionuclide. 
Inhalation of radon daughters account for 55% of the human exposure to natural sources 
of radiation (Shleien et al., 1998). Radium toxicity is related to bone sarcomas and sinus 
sarcomas due to its competition for bone with calcium. These factors as well as the fact 
that the FIPR database includes this radionuclide led to the consideration of radium-226 
as one of the points for analysis in this study. 

Original versus New Database 

There are two databases that could have been considered from the FIPR studies of 
the previous radionuclides. The original database from the 1990 FIPR report was chosen 
because the newer database has not been completed, confirmed, or published. The 
original database considered all three radionuclides and the diet model and has been in 
the literature numerous years. These reasons led to inclusion and comparison of the 
original database. 

Samples Considered 

The March 1986 FIPR report analyzed over 100 food samples, replicated up to three 
times, collected from 62 land parcels. The Phase 2 1990 FIPR report initial report 
collected and evaluated approximately 70 samples from five land parcels. These samples 



30 



were considered to determine the samples to evaluate from the stores. The samples are 
listed in Table 4-1. 



Table 4-1 : Food Samples Analyzed from Local Grocery Stores 



Beef 


1 


Beef Kidney 


1 


Black-Eyed Peas 


3 


Brazil Nuts 


1 


Brazil Nuts Shells 


1 


Broccoli 


3 


Cabbage 


3 


Carrots 


3 


Cauliflower 


3 


Collard Greens 


3 


Corn 


3 


Cucumber 


3 


Eggplant 


3 


Grapefruit 


3 


Green Beans 


3 


Greens Onions 


3 


Green Peppers 


3 


Irish Creamer Potatoes 


1 


Lemons 


3 


Lettuce 


3 


Lima Beans 


3 


Mustard Greens 


1 


Okra 


3 



Onions 


5 


Oranges 


3 


Parsley 


3 


Peas 


3 


Pole Beans 


2 


Potatoes 


3 


Purple Hull Peas 


2 


Radishes 


2 


Red Potatoes 


2 


Rice 


■5 


Spinach 




Strawberries 


-> 


Swiss Chard 


1 


Tangerine 


2 


Tomatoes 


3 


Turnip Greens 


3 


Turnip Roots and Greens 


1 


Turnip Roots 


2 


Watermelon 


2 


Yellow Corn 




Yellow Squash 


"5 


Zucchini 


3 


Total 


113 



The samples taken ranged from beef to zucchini. There were 1 13 samples total; 
45 foods were sampled. A sample is considered as a 0.5 marinela beaker filled with the 
food in question. Eight foods had only one sample; 6 foods had two samples; and the 
remainder of the foods, 31, had three samples. This provided a good average for each 
food from the three stores. 

Samples were bought from three stores in the local area to provide a better 
statistical analysis. Samples were purchased from large supermarkets to increase the 



31 

usefulness of this analysis. People outside the Gainesville area and the state of Florida 
could utilize these same data in other areas of the country. The first set of samples was 
purchased from Publix at 5200 NW 43 rd Street on 12 August 2000. Albertsons at 3930 
SW Archer Road was the site where the second set of samples was purchased on 13 
October 2000. The third store was Winn Dixie at 7303 NW 4 th Boulevard where the third 
set of samples was purchased on 20 December 2000. It is important to note that some of 
the samples only had one or two replicates. This was usually due to the limited 
availability of samples due to their seasonality. 

Location of Samples 

The samples were purchased from the various stores listed above. The question 
that should be considered is where they were grown. This is an important factor due to 
soil contamination, plant uptake, and therefore plant contamination. Samples from each 
individual store come from numerous samples, which often change daily (Greg Sciullo, 
personal communication, 30 October 2000). Even if a purchaser asks on the day the food 
is bought, the store can usually only provide the supplier and region and not the location 
at which the food was grown. This is why it is important to do this and follow-up studies 
that consider exact sources and their soil radioactivity as well as plant uptake and human 
consumption availability. 

Brazil Nuts 

Brazil nuts and Brazil nut shells were actually the first product bought sealed and 
studied. Of all the samples examined, they had the most number of peaks although not all 
were identifiable. 



32 

Food Preparation 

All foods were prepared as for normal human consumption. No foods were 
cooked, and food was cleaned, cut, and sliced to fill individual containers to maximize 
weight. The foods were then fit into a 0.5-liter Marinelli beaker. The beaker was capped, 
sealed, and stored for two weeks to allow ingrowth of radon-222 and its daughter 
products to equilibrium with its parent radium-226. The sample was then weighed and 
counted on one of two high-resolution gamma ray spectrometers. The scale that samples 
were weighed on was a Mettler P2000N, Serial No. 394916. Detectors 2 and 4 were used 
for the analysis. Detector 2 is a Germanium well detector, Serial No. 22P63XC, 
University Property No. 491044 1100485. Also, a Germanium well detector, Serial No. 
1284121 1302, University Property No. 4910 AA 1 17706, is the University Property No. 
for Detector 4. The count time varied from 9 to 24 hours. Most samples were counted for 
9.5 hours. Sampled items were counted on only two of four detectors available. This was 
due to consistency of only using two detectors as well as the limited availability of the 
other detectors. 

Grocery Store Analysis 
After gamma counting the samples utilizing detectors 2 and 4 in the Environ- 
mental Engineering Sciences laboratory, a peak search was performed. Each spectrum 
was visually inspected for additional peaks that the library search did not recognize. 

Radionuclides Evaluated 

The 1990 FIPR study evaluated their samples for three radionuclides. This 
analysis considered the same three radionuclides because they are from the U-decay 



33 

series and have identifiable peaks when counted on a gamma spectroscopy system. These 
are associated with phosphate mining and are exposed to the surface and therefore may 
be taken up by plants (Guidry et al., 1986). Radium-226 decays through several short- 
lived isotopes to radon-222. Radon is a gas that accumulates in structures and can provide 
a significant contribution to an individual's dose. 

Radium-226 CRa-226) 

The radium content was calculated by summing the three peaks at 295.2, 352.0, 
and 609.4 keV. These peaks are from the Pb-210 and Bi-214 daughters. The results are 
reported in pCi/gm of material measured (pCi/g) 

Lead-210 (Tb-210^) 

The lead-210 content was calculated utilizing the 10.8 keV peak activity. The 
results are reported in pCi/gm of material measured (pCi/g). 

Potassium-40 (K-40) 

The potassium-40 (K-40) radionuclide was measured, and data are available for 
analysis but are not reported in this chapter due to the fact that they were not analyzed in 
the FIPR 1986 or 1990 report and therefore have little use in a comparison methodology. 
It is interesting to note that the 1460keV potassium-40 peak was present and easily 
identifiable in a majority of the samples. 

Correction Factor 

A correction factor based on the detector, the radionuclide, and the 45 13 standard 
was calculated. The standard has an activity of 33200 pCi. The correction factor was 



34 



determined for radium-226 by combining the counts from the three peaks: lead-214 (295 
KeV), lead-214 (352 KeV), and the Bi-214 (609 KeV) and dividing this sum by the time 
to obtain the rate of the sample in counts per second (cps). The equation for the 
calibration factor is shown below: 



Calibration factor (CF) = 4513 Activity /Measured count rate 



(Equation 4-1) 



The calibration factors were calculated and are shown in Table 4-2. 



Table 4-2: Compilation of Calibration Factors 





Pb-210 
(PCi/cps) 


Ra-226 
(Pci/cps) 


Detector 2 


3.40E+05 


1670 


Detector 4 


1.10E+05 


1664 



Calculation 

Once the counts for each sample were analyzed and the blank sample counts were 
subtracted, the number was multiplied by the correction factor and divided by the weight 
to obtain the answer in pCi/gram. The calculation is shown below: 

Concentration = (Sample (cps)-Background (cps))*CF/Weight (Equation 4-2) 



Minimum Detectable Activity 

Many of the samples returned values of zero at several of the peaks examined. 
The minimum detectable activity was calculated at each of these data points and reported 
as the actual activity. This methodology provides for a conservative dose analysis as well 
as providing a more complete analysis. 



35 



A calculation of minimum detectable concentration (MDC) is calculated by 
first calculating the limit of detection (LD), as shown below in Equation 4-3. 



Limit of Detection (LD) = 2.83 * ((Blank/(time)) m (Equation 4-3) 



The MDC is then calculated using the Equation 4-4. 

MDC (pCi/gm) - LD (cps) * CF (pCi/cps)/Weight (g) (Equation 4-4) 

Once these data were calculated, they were reported in the data as the counts. 

Output of Analysis 

Figure 4-1 shows a sample output from the Gamma Vision Program utilized to 
count the various samples. An output report similar to this one was produced for each 
individual sample. A spectrum was also printed out to allow a visual observation and 
comparison with other samples. 



Detector #4 ACQ 


09-Sep- 


00 


at 9:05 


:03 


RT = 34200 





LT = 34187.1 




Detector 


# 4 HPGe 


End Cap 


in Green Shield 








Beef 09/09/2000 


















ROI# RANGE ( keV) 


GROSS 




NET 


CENTROID FWHM 


FW(1/10) LIBRARY ( keV) 


Bq 


1 72.11 79.55 


1190 




297 


71 


76.91 





59 


1.35 No close library 


match . 


2 256.31 261.13 


354 




-25 


34 


258.66 


C 


3? 


0.71 No close library 


match. 


3 522.34 526.95 


457 




221 


30 


524.76 





65 


2.91 No close library 


match. 


4 623.75 626.36 


145 




56 


13 


624.77 


1 


22 


1.74 No close library 


match. 


5 1492.05 1497.04 


959 




768 


37 


1494.45 


2 


11 


3.73 No close library 


match. 



Figure 4-1 : Sample Report for Beef 

Results and Analysis 

Appendix A illustrates, in tabular form, the raw data that provided the dose 
determination. Peak information was determined from reports similar to Figure 4-1 . 
These were output from the library search performed on each spectrum measured from 



36 

each sample. Appendix B contains the Crystal Ball analysis charts for the various 
analyses performed. 

Table 4-3 lists the results for this analysis. As can be observed from these data, 
cucumbers show the highest lead-210 concentration at 47 pCi/g. Beef was observed to 
have the lowest lead-210 concentration at 0.076 pCi/g. Potatoes, rice, beef kidney, and 
watermelon show the lowest radium-226 concentration with 0.002 pCi/g. Parsley had the 
highest observed concentration at 0.029 pCi/g. 

Table 4-3: Gamma Spectroscopy Analysis of Local Grocery Samples 





Averages (pCi/g) 


Item 


Pb-210 


Ra-226 


Beef 


0.076 


0.004 


Beef Kidney 


0.357 


0.002 


Black-Eyed Peas 


0.494 


0.003 


Brazil Shells 


1.021 


0.003 


Broccoli 


0.829 


0.005 


Cabbage 


0.858 


0.006 


Carrots 


0.555 


0.004 


Cauliflower 


1.466 


0.005 


Collard Greens 


1.372 


0.006 


Corn 


0.506 


0.006 


Cucumber 


47.082 


0.009 


Eggplant 


1.425 


0.006 


Grapefruit 


0.096 


0.005 


Green Beans 


3.837 


0.007 


Green Onions 


0.852 


0.014 


Green Peppers 


0.431 


0.004 



Irish Creamer 
Potatoes 


0.120 


0.006 



Lemons 


0.414 


0.005 


Lettuce 


1.237 


0.004 


Lima Beans 


0.963 


0.003 


Mustard Greens 


1.622 


0.017 


Okra 


1.072 


0.003 


Onions 


0.599 


0.004 





Averages (pCi/g) 


Item 


Pb-210 


Ra-226 


Oranges 


0.682 


0.003 


Parsley 


7.378 


0.029 


Peas 


0.821 


0.003 


Pole Beans 


0.704 


0.004 


Potatoes 


0.846 


0.002 


Purple Hull Peas 


0.454 


0.003 


Radishes 


0.580 


0.004 


Red Potatoes 


0.215 


0.003 


Rice 


0.654 


0.002 


Spinach 


0.422 


0.020 


Strawberries 


0.715 


0.004 


Swiss Chard 


2.010 


0.006 


Tangerine 


0.686 


0.004 


Tomatoes 


1.011 


0.003 


Turnip Greens 


0.941 


0.006 


Turnip Root and Green 


1.841 


0.005 



Turnip Roots 


0.941 


0.006 



Watermelon 


0.776 


0.002 


Yellow Corn 


0.680 


0.005 


Yellow Squash 


0.613 


0.004 


Zucchini 


0.108 


0.005 


Brazil Nuts 


1.324 


0.007 



37 

The average for lead-210 for all samples is 2.037 pCi/g. This value is higher than 
most due to the largest value increasing the value. All of the samples have concentrations 
below this value with the exception of parsley and cucumber. The average for Ra-226 is 
0.006 pCi/g. Fifteen sample concentrations lie on or above this value with all others 
measured below. Brazil nuts and their shells cause this value to be higher than most of 
the measured values. The concentration of mustard greens lies at this value, and all other 
concentrations lie below this value. 

Rice Experimental Analysis 
Determination of the distribution associated with the concentration of 
radionuclides in food was undertaken with the following results. The distribution of a 
radionuclide concentration in a food was approached utilizing two major methods: 
experimentally and with a review of relevant literature current studies. 

Review of Literature and Current Studies 

The 1986 FIPR report initially assumed a lognormal distribution. The subsequent 
pilot study and analyses utilizing a residual test bore out this hypothesis. This was 
performed primarily for radium-226 in the various food items for the study. The study 
analyzed 3 1 food items in six general categories. 

The subsequent 1990 study and the current research agree with the initial analysis 
from the 1986 paper. The findings were for a lognormal distribution, which was 
determined by analyses of the data distribution for specific food items grown on each 
land analyzed for each radionuclide. 



38 

Experimental Analysis 

Even though these data seem conclusive in one method to assume a lognormal 
distribution, they do not address the point of different food items, especially the grocery 
items. This chapter deals with research performed on grocery store items, whereas the 
previous studies did not. The 1990 FIPR report (Guidry et al., 1990) analyzed one sample 
of each food type but could not perform any relevant or applicable analyses on only that 
one data point. This chapter dealt with 3 data points (in most cases) from each food type. 

An analysis was undertaken to analyze a food type for the distribution. The results 
obtained, although numerical in nature, were essentially qualitative. The determination of 
distribution was obtained through measurement and analysis of rice obtained from Publix 
and measured for a single radionuclide. 

Choice of Food Sample 

The rice was purchased from Publix on 4 February 2001. The brand chosen was 
Publix' own brand. This was chosen both for the price consideration as well as the 
probability of consumption due to the limited cost by an average consumer. Rice was 
chosen also because it provided a consistently high potassium-40 peak on prior analyses. 
This provided a good indication that this sample would provide a good consistent peak to 
analyze on all samples measured. 

Preparation 

Similar to all the experimental analysis for this research, the 20 samples of rice 
were placed in Marinelli beakers. Each 0.5 beaker was filled with rice, sealed and 
refrigerated for two weeks to allow for ingrowths of the Radon daughters to equilibrium. 



39 

Measurement 

The samples were weighed after the two-week period. Each sample was then 
measured on one of two high purity GeLi detectors. Detectors 2 and 4 were chosen for 
this analysis due to their previous utilization with other samples as well as their 
availability. The samples were each measured for 9-1/2 hours. Once again, this time was 
chosen to provide an opportunity for future comparison with other data obtained in this 
research. 

Comparison 

The spectrums of the samples, once counted, were individually examined to 
ensure the potassium-40 peak was observed and analyzed. As expected, the peak was 
found on every sample to varying degrees. An analysis of the data was performed on the 
10 samples measured on each detector as well as overall for all 20 samples. 

Results 

These data were analyzed for several statistical attributes, such as skewness, 
maximum, minimum, kurtosis, range, and standard deviation. Tables 4-4, 4-5, and 4-6 
show the summary statistics for detector 2 and detector 4. A comparison of the raw data 
and these numbers illustrate that one point on detector 4 was an outlier. Tables 4-7 and 4- 
8 show the same statistical comparisons for the combined data with and without the 
outlier, respectively. 

A survey of the statistics from detector 2 (Table 4-4) shows that the range of 
counts per second per gram for the samples measured was 3.36 * 10" 6 . The mean of all 
samples on these detectors was 5.83 *10" 6 . The standard deviation was 1 *10" 6 . The 



40 



skewness, a measure of the distribution to deviate from a standard distribution, is 0.378. 
This supports the contention of the literature cited above that states that the distribution of 
radionuclide concentration of food is lognormal, in this case positively skewed. 



Table 4-4: Summary of Rice Sample Statistics from Detector 2 



SUMMARY STATISTICS DETECTOR 2 



Mean 

Standard Error 

Median 

Standard Deviation 

Sample Variance 

Kurtosis 

Skewness 

Range 

Minimum 

Maximum 

Sum 

Count 

Largest (1) 

Smallest (1) 

Confidence Level (95.0%) 



5.82591E-06 
3.18389E-07 
5.71661E-06 
1.00684E-06 
1.01372E-12 
-0.165870891 
0.378137914 
3.36092E-06 
4.26156E-06 
7.62247E-06 
5.82591E-05 
10 

7.62247E-06 
4.26156E-06 
7.20248E-07 



Table 4-5 shows similar statistics for the samples measured on detector 4. The 
outlier is included in this analysis for the sake of comparison and to illustrate the effect 
that the outlier has on the analysis. The mean of the data with the outlier is 5.05*10" 6 . The 
standard deviation is 1.6 *10" 6 . The range is 5.96* 10" 6 . This number is close to twice as 
large as the range associated with detector two samples. The mean was measured as 
S.OS'MO" 6 and the skewness as -1.25*10" 6 . This is not only larger but in the opposite 



41 

direction to the distributions both researched and assumed. An observation of the raw 
data illustrated that one data point, 1 .3* 1 0" 6 was an outlier. Once this was removed, Table 
4-6 was obtained and analyzed. 



Table 4-5: Summary of Rice Sample Statistics from Detector 4 

SUMMARY STATISTICS OF RICE SAMPLES ON DETECTOR 4 



Mean 

Standard Error 

Median 

Standard Deviation 

Sample Variance 

Kurtosis 

Skewness 

Range 

Minimum 

Maximum 

Sum 

Count 

Largest (1) 

Smallest (1) 

Confidence Level (95.0%) 



5.05372E-06 
5.16785E-07 
5.21956E-06 
1.63422E-06 
2.67067E-12 
2.670178378 
-1.254131791 
5.96386E-06 
1.29724E-06 
7.261 1E-06 
5.05372E-05 
10 

7.261 1E-06 
1.29724E-06 
1.16905E-06 



Table 4-6 illustrates that with the outlier removed, the mean is now higher at 
5.5 *10" 6 . The standard deviation has now been reduced to 1.02*10" 6 . The range is now 
3.25 * 10" 6 , less than detector 2. The skewness measured a +0.37, which is very close to 
that measured for detector 2. These data, with the outlier removed, tend toward a 
lognormal distribution due to the skewness measured and the similarity of data obtained 
from both sets of samples. 



42 



Table 4-6: Summary of Rice Sample Statistics without Outlier from Detector 4 
SUMMARY STATISTICS ON DET 4 WITHOUT OUTLIER 



Mean 

Standard Error 

Median 

Standard Deviation 

Sample Variance 

Kurtosis 

Skewness 

Range 

Minimum 

Maximum 

Sum 

Count 

Largest (1) 

Smallest (1) 

Confidence Level (95.0%) 



5.471 11E-06 
3.40689E-07 
5.52044E-06 
1.02207E-06 
1.04462E-12 
-0.449095314 
0.37326003 
3.25132E-06 
4.00978E-06 
7.261 1E-06 
4.924E-05 
9 

7.261 1E-06 
4.00978E-06 
7.8563 1E-07 



An analysis was undertaken to compare the same statistics on both data sets 
combined. There were two analyses performed, one with the outlier and one without the 
outlier. These are shown in Table 4-7 and 4-8. 

Table 4-7 illustrates the summary statistics on the rice samples measured from 
both detectors combined. Consideration of the outlier would provide a mean of 5.4* 10" 6 . 
A standard deviation would be obtained that would be 1 .38* 10" 6 . The range would be 
6.3* 10" 6 with the minimum and maximum measured at 1.3*10" 6 and 7.6* 10" 6 , 
respectively. The skewness would be a - 1 .2* 1 0" 6 . All of this, as well as the data from 
detector 4 above, details a reasonable justification for removing the outlier and 
considering the other 19 data points as the total sample. 



43 



Table 4-7: Summary of Rice Sample Statistics: Total Rice Samples 

STATISTICS-ALL DATA POINTS "" 

Mean 5.43981E-06 

Standard Error 3.08395E-07 

Median 5.49973E-06 

Standard Deviation 1 .3791 8E-06 

Sample Variance 1.90215E-12 

Kurtosis 3.328489995 

Skewness -1.201595498 

Range 6.32524E-06 

Minimum 1.29724E-06 

Maximum 7.62247E-06 

Sum 0.000108796 
Count 20 

Largest (1) 7.62247E-06 

Smallest (1) 1.29724E-06 

Confidence Level (95.0%) 6.45478E-07 



Utilizing the other 19 data points and performing a summary analysis, Table 4-8 
is obtained. As can be observed from Table 4-8, similar to the observations from Table 4- 
6, the mean has now increased to 5.7* 10" 6 . The standard deviation has now decreased to 
1.0* 10" 6 . The range, S.6*^" 6 is essentially half of that obtained with the outlier in Table 
4-7, and the skewness was increased to a positive 0.32* 10" 6 , once again supporting the 
data obtained by the two sources in the literature search from analyses of previous data. 

Histogram Analysis 
A histogram analysis was performed on the various sets of data prior to the 
summary statistics that were derived above. These initial analyses were performed to 
provide a visual representation of the data and their subsequent distributions. They have 
been included here to provide for a more complete data analysis as well as to show how 
the outlier was initially found. Figure 4-2 shows the data plotted in a histogram. The 



44 



outlier lies to the left-hand side of the plot, conspicuously alone. Further consideration 
required determination of which detector and sample this number was obtained. 

Table 4-8: Summary of Rice Sample Statistics: Total Rice Samples without Outlier 



COMBINED STATS EXCLUDING OUTLIER 



Mean 5.65784E-06 

Standard Error 2.29904E-07 

Median 5.52044E-06 

Standard Deviation 1 .002 1 3E-06 

Sample Variance 1 .00426E- 1 2 

Kurtosis -0.512673412 

Skewness 0.318703287 

Range 3.61269E-06 

Minimum 4.00978E-06 

Maximum 7.62247E-06 

Sum 0.000107499 

Count 19 
Largest (1) 7.62247E-06 

Smallest (1) 4.00978E-06 

Confidence Level (95.0%) 4.8301 1E-07 



Figures 4-3 and 4-4 show Detector 2 and 4 rice sample histograms, respectively. 
Figure 4-3 shows all data in a close grouping and range, whereas the histogram of 
detector 4 has a similar grouping with the notable exception of one data point. 

The detector 4 histogram has a larger range than that presented on the histogram 
of detector 2. The grouping of detector 2 has a much smaller range when the outlier is 
excluded. This was the first indication that there was a point that should be removed in 
the consideration of the data. Removing this data point and replotting detector 4 rice 
samples in a histogram reveals Figure 4-5. 



45 

This histogram reveals the reduced range similar to that obtained with the samples 
from detector 2. The grouping could be lognormal or normal. A histogram of all samples 
as well as a statistical summary analyses performed above is a more accurate indicator of 
distribution. Figure 4-6 shows the histogram of the entire data set with the exception of 
the outlier. 



Histogram of AD Rice Samples 





*t.o - 

4- 
3.5- 

3- 
2.5- 

2- 
1.5- 

1 - 
0.5- 

0- 












o 








c 

0) 












3 












? 


1 








1 


U. 


I 








H 




1 1 








— 1 ! ' 




1 1 

r™ -i 1 1 1 1 1 M i B 


i 


i 


■ 


___■_■_ | | t 1 1 



* r*> .<£ c* rfc 



& ,& .& 



fJ •.• SSSJ ^ J 



^ <? o* 



*~ <D V <b V A V %? <* 



Counts/Second/Gram 



^ ^ 



Figure 4-2: Histogram of All Rice Samples 



3.5 
3 

2.5 
§ 2 

1 1-5 

£ 1 

0.5 





Histogram Detector 2 




*& <,& ,& 



C# 



& 







& 



<b- 



^ 



<& 



& 



A-' 



.# 



Counts/Second/Gram 



«* • 



Figure 4-3: Histogram of Detector 2 Samples 



46 



3.5 

3 

j? 2.5 

I 2 
I 1.5 

u. 1 

0.5 





i.g.| ~ 



Histogram Detector 4 




Counts/Second/Gram 



Figure 4-4: Histogram of Detector 4 Samples 



^ / / / / /' / J" * 



3.5 
3 

2.5 
2 



g" 15 



u. 



>» 
o 

c 

0) 

3 



1 

0.5 





Histogram Detector 4 excludhg outlet 



E 



1 






# J§> 



I 



» J* 



C? rK> <£> rS> <S 

J- / /" / /" /■ / ^ /" 

Counts/Secontf G ram 



Figure 4-5: Histogram of Rice Samples on Detector 4 excluding Outlier. 



This curve illustrates a bimodal distribution around 6*10" 6 counts/gram/sec and 
has a slightly lognormal appearance. The distribution at this point was determined using 
the summary statistical analysis to ensure that the outlier removal was justified and to 



47 



determine the shape of the distribution. Additionally, the data were analyzed using the 
Crystal Ball program to determine that the distribution, though limited in number of data 
points, most closely approximates a lognormal distribution. 



Histogram of All Rice Samples 




f j? • 



Counts/Second/Gram 



Figure 4-6: Histogram of All Samples excluding Outlier 



Conclusion and Recommendations for Future Research 
Analyses were performed on 20 rice samples obtained from Publix Supermarket 
in Gainesville, Florida. The 20 samples were tested on detector 2 and detector 4 of the 
gamma spectroscopy laboratory at the environmental Engineering Sciences Department 
at the University of Florida. The goal of this portion of the research was to determine 
qualitatively what type of distribution is exhibited by concentration of radionuclides in 
foods. A literature search was performed providing information specific to foods grown 
on phosphate related lands. These data stated that the distribution followed a lognormal 
distribution. The analyses on these samples, with histograms and summary statistics, 
proved that one of the data points was an outlier and, when excluded, provided good 



48 

agreement with the data obtained from the previous research. The concentration of 
radionuclide in food studied in this set of analyses followed a lognormal distribution. 

Further research should be undertaken, both in the form of a literature search and 
experimentally, to determine if this is accurate for a wider range of foods. Studies should 
be performed to determine how the distribution changes by store, location, and land type. 
Additionally, the data presented here should also be examined utilizing the residuals 
method to confirm, with another method, how the data best fit this distribution. Another 
analysis, with more data points, should be undertaken to determine the distribution with 
better accuracy. 

The above experimental data on grocery store foods was determined utilizing 
previous studies as a template as well as a guideline to choose which samples to measure. 
Brazil nuts, although not in the original work, prove to be hyper accumulators. They 
exhibit the highest number of peaks of any measured food. Their shells also exhibit the 
same properties. Beef and beef kidney are only one data point and will not be used for the 
analysis to follow. An interesting point to note about beef is that it illustrates a low lead- 
210 concentration whereas the kidney shows a high lead-210 concentration. The data 
examined as a whole illustrate that the concentration of radium-226 is lower, on average, 
than lead-210. 

This chapter has laid down the concentration and associated distributions of 
various radionuclides in specific grocery store foods. The previous chapter determined 
dietary intake and the distribution that it is estimated to follow. The next in this series of 
chapters deals with the dose conversion factor. The data from these three chapters will be 



49 



combined in the sixth chapter on dose to provide a more accurate estimate both in 
number and shape of distribution than currently available in the literature. 



CHAPTER 5 
DOSE CONVERSION FACTORS 



Introduction 
This is the fifth in a series of chapters designed to design and implement a 
methodology to determine a probabilistic radiation dose to individuals from foods 
bought at local stores in Gainesville, Florida, using the Crystal Ball program. The first 
chapter provided the introduction of a probabilistic dose approach. The second chapter 
described the literature search for the overall dissertation to determine the references 
that were used for each section. The third chapter determined the dietary intake values 
to be used and the most probable distribution to describe them. The fourth chapter 
described the actual experimentation performed to determine both the concentration of 
specific radionuclides in the various foods measured and the distribution to describe this 
concentration. The purpose of this chapter is to determine the value and distribution to 
describe the dose conversion factor. 

Literature Search 
A literature search was performed to determine the various applicable references 
in an effort to determine the correct dose conversion factor (DCF) as well as a 
distribution to apply to it. The data for the dose conversion factor (DCF) came from 
four sources. The first source was Federal Regulatory Guide number 1 1 (EPA, 1988). 
This document provides the methodology used to calculate the DCFs for inhalation 



50 



51 

submersion, and ingestion. The tables of the various DCF data for various radionuclides 
are included in this manual. 

The articles International Council on Radiation Protection (ICRP) 68 (ICRP, 
1994) and 72 (ICRP, 1996) provide age-dependent DCFs for workers and members of 
the public from intake of radionuclides. 

The fourth reference for these data was a solution manual that calculated a dose 
conversion factor for strontium 90 (Turner, Bogard, Hunt, & Rhea, 1988, pp. 96-101). 
This was utilized as a reference to describe the method to obtain a dose per unit intake 
factor from the initial data. 

It should be noted that an additional vital source of information describing the 
distribution was a direct conversation with Dr. Eckerman at Oak Ridge National 
Laboratories. He provided the data that stated that the dose conversion factors follow a 
lognormal distribution. Lead-210 and radium-226 distribution encompass 90% of the 
values by multiplying and dividing the mean by a factor of five. Polonium-210 
distribution can encompass 90% of the values by multiplication and division of the 
mean by a factor of 10. These data were incorporated into the final analysis of each 
dose analysis as the ninth case. 

Discussion 
There are two points which need to be addressed at this point: the distribution 
and the method to obtain or make an educated estimate and the different sources of 
DCFs. Either a distribution can be assumed or it can be calculated utilizing the Crystal 
Ball analysis to assign distributions to each of the variables in the equation. Either 
approach will produce a final output that will be utilized in the next chapter to calculate 



52 

and derive a distribution for the end product dose. The purpose of this chapter is to 
derive a probabilistic methodology that can predict a distribution for dose. 

There are at least three different sources of dose per unit intake or dose 
conversion factors: the EPA Federal Regulatory guide (FRG) number 11, International 
Council on Radiation Protection (ICRP) Publication 68 and ICRP 72. These sources and 
their DCFs are listed in Table 5-1. 

Table 5-1: Dose conversion Factors from Various Sources (Sv/Bq) 





ICRP 68 


ICRP 72 


FRG 11 


Pb-210 


6.80e-7 


6.90e-7 


1.450e-6 


Ra-226 


2.80e-7 


2.80e-7 


3.58e-7 


Po-210 


2.40e-7 


1.20e-6 


5.14e-7 



As can be seen from this table, the numbers are not identical and have a rather 
large variance. The dose conversion factors from Federal Regulatory Guide Number 1 1 
were utilized in this report. These data were chosen to maintain consistency with 
previous reports and to provide comparability with data from those same reports. 



Conclusion and Recommendations 

The above data for the EPA FRG number 1 1 will be utilized for the purpose of 
this report with the distribution to be assigned as a lognormal distribution. The EPA 
FRG 1 1 dose conversion factors will be converted to mrem/pCi to maintain consistency 
and units. 

A suggestion for future work is twofold. The discrepancies between the various 
agencies and their dose per unit intake should be considered and evaluated. 
Additionally, the distribution for this factor should be evaluated utilizing Crystal Ball 



53 

and the individual factors in the equation to obtain a more accurate determination of the 
distribution for this factor. 

The next chapter combines all the previous data and distributions together. The 
original 1990 FIPR (Guidry et al., 1990) study is analyzed for a series of distributions 
for each of the parameters. Two radionuclides are considered: radium-226 and lead-210. 
The resulting Crystal Ball dose distributions are presented in tabular format. A similar 
analysis is performed on the grocery store data for each radionuclide. The last chapter 
sums all the previous data into a combined whole for comparison and discussion. 



CHAPTER 6 
COMMITTED EFFECTIVE DOSE EQUIVALENT 

Introduction 

This chapter designed to determine and test a methodology to calculate a 
probabilistic radiation dose to individuals from foods bought at local stores in 
Gainesville, Florida. The first chapter provided the introduction of a probabilistic dose 
approach. The second chapter described the literature search for the overall dissertation to 
determine the references that were used for each section. The third chapter determined 
the dietary intake values to be used and the most probable distribution to describe them. 
The fourth chapter described the actual experimentation performed to determine both the 
concentration of specific radionuclides in the various foods measured and the distribution 
to describe this concentration. The fifth chapter described the methodology to determine 
the dose conversion factor (DCF) value and distribution. The purpose of this chapter is to 
determine the value and distribution to describe the dose to an individual based on the 
values obtained in the previous chapters. 

This purpose will be accomplished by a literature search that describes the 
applicable and relevant literature to determine the committed effective dose equivalent, 
the term to describe the extended dose to an individual based on intake of a specific 
radionuclide. The data previously obtained were then analyzed with the original data and 
comparison is provided. 



54 



55 

Literature Search 

Dose to an individual can be calculated in several ways. The EPA Federal 
Regulatory Guide Number 1 1 provides the dose conversion factors utilized in this chapter 
(EPA, 1988). Other dose conversion factors from ICRP 68 (ICRP, 1994) and ICRP 72 
(ICRP, 1996) were considered but not utilized for this analysis. This was to maintain 
consistency from the previous 1990 Florida Institute of Phosphate Research (FIPR) 
report. These tables allow the user to calculate a dose to an individual based on the 
individual's unit intake of a radionuclide. 

The 1990 FIPR report was utilized for its diet model and dose analysis of radium- 
226 and lead-210 (Guidry et al., 1990). The dose analysis from this report was utilized to 
determine the associate dose and distribution to a known and published value for a diet of 
an individual living in Florida. The dose model considered from this paper was only the 
debris land model for each radionuclide owing to the fact that the maximum individual in 
this category had the highest dose. 

Method 
Determination of dose to an individual is accomplished by integrating the 
information determined in the previous papers, multiplying the appropriate factors, 
summing, and then running Crystal Ball on the entire set to determine an output. 
Equation 1-1 illustrates the formula to calculate dose to an individual. Each variable in 
this formula is assigned a value in a Microsoft Excel spreadsheet. The various values for 
intake, concentration, and dose conversion factors are assigned a distribution from the 
Crystal Ball library. Crystal Ball, produced by Decisioneering, is a program addition to 
Microsoft Excel (Decisioneering, 1996). This program utilizes a Monte Carlo sampling 



56 

technique for each assigned distribution to determine a final dose in the form of a 
distribution. 

Monte Carlo is a method in which a random sample is picked from each 
distribution and used in the calculation. Each random sampling, with its resultant output, 
is called a trial. Depending on the number of trials specified, an output distribution is 
framed. The more trials performed, the more accurate the distribution. 

Specific fluctuations in the variables such as location of individuals, eating habits, 
land type, where food is grown, radiation type and food preparation methods are taken 
into account by the distribution determination in each variable. Specific errors are 
considered as a whole to contribute to the shape of the distribution. A family of 
distributions and analyses are performed to ensure flexibility of the resultant output in 
determination of a final dose. Should one specific set not be correct in its distribution 
choice, other sets will allow the correct determination of dose and associated 
distribution. 

Nine sets of analyses were performed on each radionuclide, lead-210, and radium- 
226. These analyses were performed on the original 1990 FIPR report and the 
experimentally obtained grocery store data. The data are presented in tabular format, 
comparing the different distributions uses and the different distributions obtained for each 
set. The sets of data are presented below in Table 6-1 . 

The various sets each have different values for intake, concentration, and dose 
conversion factors. LN represents a lognormal distribution, and G represents a gaussian 
distribution. The intake values for each variable were obtained from the previous 
chapters. The intake values were obtained from the 1990 FIPR report and the third report 



57 



in this series. The concentration data were taken from the fourth chapter, the 
experimental analyses on the grocery store samples and from the 1990 FIPR report. The 
dose conversion factors were obtained from Federal Regulatory Guide #11. Default 
values were utilized for the various parameters that could not be identified. Set nine is a 
special case that is similar to set 1 with the exception that the dose conversion factor is 
specified by a more exact representation of the actual DCF. Set 9 is the most plausible 
scenario for the dose value and distribution. All Crystal Ball analyses were run with 
20,000 trials to improve consistency, accuracy, and comparability. 

Table 6-1 : Sets of Distributions Utilized in Analyses on Data 







Intake 


Concentration 


DCF 


Set 


1 


LN 


LN 


LN 


Set 


2 


G 


LN 


LN 


Set 


3 


G 


G 


LN 


Set 


4 


G 


G 


G 


Set 


5 


LN 


G 


G 


Set 


6 


LN 


LN 


G 


Set 


7 


LN 


G 


LN 


Set 


8 


G 


LN 


G 


Set 


9 


LN 


LN 


LN 



Analysis of 1990 FIPR Dose Diet 
Radium 226 Analysis on 1990 FIPR Data 

The dose worksheet provided in Table 6-2 shows the spreadsheet for the radium- 
226 dose calculation that was used as input to the Crystal Ball program. Each of the 
intake variables and concentration variables were assigned a distribution. The dose 



58 



Table 6-2: Input Spreadsheet Data for Radium 226 Dose Calculation (Guidry et al., 1990) 





DCF 1.30E-03 (mrem/pCi) 


Diet Item 


Intake 
(g/day) 


Concentration 
(pCi/kg) 


Intake 
(PCi/yr) 










Broccoli 


3.51 


34.67 


44.42 



LEAFY 



Cabbage 


7.04 


32.2 


82.74 


Collard Greens 


0.45 


86.23 


14.16 


Lettuce 


23.38 


45.41 


387.52 


Mustard Greens 


0.45 


64.22 


10.55 


Spinach 


3.28 


540.25 


646.79 


Turnip Greens 


0.45 


55.47 


9.11 



SEEDS/GRAINS 



Blackeyed Peas 


5.61 


25.6 


52.42 


Rice 


22.94 


82.18 


688.10 


Yellow Corn 


14.41 


25.6 


134.65 



ROOTS 



Carrot 


2.92 


113.83 


121.32 


Onion 


4.19 


33.3 


50.93 


Radish 


0.32 


33.3 


3.89 


Turnip 


0.42 


23.64 


3.62 



GENERAL 



Cucumber 


2.62 


18.6 


17.79 


Green Beans 


8.8 


9.79 


31.45 


Green Peppers 


1.99 


18.6 


13.51 


Strawberries 


1.23 


806.68 


362.16 


Tomato 


25.18 


18.6 


170.95 


Watermelon 


3.44 


18.6 


23.35 


Squash/Zucchini 


1.26 


5.15 


2.37 


Totals 


133.89 




2871.78 


Total Diet 


3071.81 





Dose 



Non-Sampled 



2. 18E+00 mrem/yr 



Sampled 



3.73E+00 mrem/yr 



Total 



5.92E+00 mrem/yr 



59 

conversion factor was also assigned a distribution. The product of these three variables 
and a conversion factor allowed the determination of a dose and a distribution. 

Table 6-3 shows the output of the family of analyses obtained when the various 
distributions were placed into the appropriate variables. Table 6-4 illustrates the statistical 
data to allow for a comparison of the various distributions. 

Figure 6-1 is the output of the Crystal Ball forecast for set 9. Figure 6-2 shows the 
difference comparison between the best fit distribution and the Monte Carlo Crystal Ball 
determination of the distribution. The scale on the y-axes illustrates that there was close 
agreement. 

Table 6-3: Table of Input and Output Distributions for Radium-226 







Intake 


Concentration 


DCF 


Dose 


Set 


1 


LN 


LN 


LN 


LN 


Set 


2 


G 


LN 


LN 


LN 


Set 


3 


G 


G 


LN 


LN 


Set 


4 


G 


G 


G 


G 


Set 


5 


LN 


G 


G 


Beta 


Set 


6 


LN 


LN 


G 


Beta 


Set 


7 


LN 


G 


LN 


LN 


Set 


8 


G 


LN 


G 


Beta 


Set 


9 


LN 


LN 


LN 


LN 



Table 6-4: Statistical Comparison of Various Data for Radium-226 







Mean 


Std Dev 


Skewness 


Kurtosis 


COF 


Range Width 


Set 


1 


5.91 


0.623 


0.3 


3.17 


0.11 


4.81 


Set 


2 


5.92 


0.625 


0.32 


3.13 


0.11 


5.16 


Set 


3 


5.92 


0.632 


0.3 


3.15 


0.11 


5.1 


Set 


4 


5.92 


0.629 


0.06 


3.04 


0.11 


4.91 


Set 


5 


5.92 


0.627 


0.05 


3.04 


0.11 


5.12 


Set 


6 


5.92 


0.626 


0.05 


2.97 


0.11 


4.62 


Set 


7 


5.91 


0.624 


0.32 


3.3 


0.11 


6.23 


Set 


8 


5.92 


0.624 


0.08 


3.04 


0.11 


5.28 


Set 


9 


9.56 


12.1 


5.08 


53.59 


1.26 


270 



Overlay Chart 
Frequency Comparison 




Icgxrrrd Dstrfaicn 

l\fen=9S£K) 

SbDB/=12IEH 



Tea 



QOCBO 



112&1 



22&1 



33E&1 



43&1 



60 



Figure 6-1 : Set 9 Output and Distribution Fit for Ra-226 



Overlay Chart 
Frequency Dfference 



.OB 




-OB 



• 




■ 




III 


■1 1 1.1 1 1 1 J 1 1 1. . .1 il.l ii, 


• 1 


IT 


l|. .||.| ii i -■ ■ i| |i |'v.-"."r 


• 




• 



Lcgtjrrd Dstrixticn 

Mai=95E&0 

StlDa/=121&1 



TcH 



QCCBO 



112&1 



225&1 



33E&1 



45B-1 



Figure 6-2: Difference Chart for Ra-226 Set 9 



Lead-210 Analysis on 1990 FIPR Data 

The lead-210 analyses on the 1990 FIPR data was performed in the same manner as 
the radium-226 above. The input data, represented in spreadsheet form, is presented in 
Table 6-5 below. Table 6-6 is the presentation or the distribution data for the various 



61 



Table 6-5: Input Spreadsheet Data for Lead-210 Dose Calculation (Guidry et al., 1990) 





DCF 


5.40E-03 


(mrem/pCi) 


Diet Item 


Intake 
(g/day) 


Concentration 
(pCi/kg) 


Intake 
(PCi/yr) 










Broccoli 


3.51 


60.09 


76.98 



LEAFY 



Cabbage 


7.04 


122.61 


315.06 


Collard Greens 


0.45 


33.29 


5.47 


Lettuce 


23.38 


75.56 


644.81 


Mustard Greens 


0.45 


0.50 


0.08 


Spinach 


3.28 


166.49 


199.32 


Turnip Greens 


0.45 


40.48 


6.65 



SEEDS/GRAINS 



Blackeyed Peas 


5.61 


22.00 


45.05 


Rice 


22.94 


62.26 


521.31 


Yellow Corn 


14.41 


22.00 


115.71 



ROOTS 



Carrot 


2.92 


5.97 


6.36 


Onion 


4.19 


4.70 


7.19 


Radish 


0.32 


4.70 


0.55 


Turnip 


0.42 


10.22 


1.57 



GENERAL 



Cucumber 


2.62 


8.00 


7.65 


Green Beans 


8.80 


8.00 


25.70 


Green Peppers 


1.99 


8.00 


5.81 


Strawberries 


1.23 


456.19 


204.81 


Tomato 


25.18 


8.00 


73.53 


Watermelon 


3.44 


8.00 


10.04 


Squash/Zucchini 


1.26 


8.00 


3.68 


Totals 


133.89 




2277.31957 


Total Diet 


3071.81 





Dose 



Non- Sampled 



9.07E+00 mrem/yr 



Sampled 



1.23E+01 mrem/yr 



Total 



2.14E+01 mrem/yr 



62 



Table 6-6: Table of Input and Output Distributions for Lead-210 







Intake 


Concentration 


DCF 


Dose 


Set 


1 


LN 


LN 


LN 


LN 


Set 


2 


G 


LN 


LN 


LN 


Set 


3 


G 


G 


LN 


LN 


Set 


4 


G 


G 


G 


Beta 


Set 


5 


LN 


G 


G 


Beta 


Set 


6 


LN 


LN 


G 


G 


Set 


7 


LN 


G 


LN 


LN 


Set 


8 


G 


LN 


G 


Beta 


Set 


9 


LN 


LN 


LN 


LN 



variables and the final dose. Table 6-7 shows the statistics of interest for the output 
distributions. 

Figure 6-3 is shown as the set 9 for this family of distribution analyses. It is 
believed to be the most probable outcome of dose. Figure 6-4 shows the Crystal Ball 
output graph of the difference chart. This graph illustrates the difference between the 
output dose distribution and the closest fit approximation determined by the program and 
its subsequent Chi-squared test of fit for the curve. 

Table 6-7: Statistical Comparison of Various Data for Lead-210 







Mean 


Std Dev 


Skewness 


Kurtosis 


COF 


Range 
Width 


Set 


1 


21.4 


2.25 


0.32 


3.18 


0.11 


17.6 


Set 


2 


21.4 


2.25 


0.29 


3.1 


0.11 


18.2 


Set 


3 


21.3 


2.25 


0.37 


3.27 


0.11 


19.6 


Set 


4 


21.3 


2.25 


0.06 


3.04 


0.11 


18.4 


Set 


5 


21.4 


2.27 


0.05 


3.06 


0.11 


19 


Set 


6 


21.3 


2.28 


0.08 


2.99 


0.11 


19 


Set 


7 


21.4 


2.25 


0.33 


3.18 


0.11 


18.2 


Set 


8 


21.4 


2.28 


0.07 


3.05 


0.11 


18.1 


Set 


9 


34.7 


43.9 


5.18 


56.66 


1.25 


965 



63 



Overlay Chart 
Frequency Comparison 




QCCBO 



37»1 



73EM 



nmuBBB 

1.12&2 



liy tiirrf DstrhJian 
l\*an=347&1 

aJQ*=43£-1 



TcB 



1.5&2 



Figure 6-3: Set 9 Output and Distribution Fit for Pb-210 



Overlay Chart 
Frequency Dfferaxe 



.OCB-f 



.GDI 

.ODD 
-JDD1 
-JDD3 



■ 




III 


IJL-sju 


. 1 . ll .In I.I .1 1. ., ,. . 1 . 1 . . 


pi 


1 | |||| |'|| -I i 1 ■■!■! || II- | ■ -- • •■■ -i ■ i. ■ 


■ 





Lyund Qstrititjcn 

N*m=345&1 

ajQy=43&1 



TcH 



QCC&O 



37&1 



7.3B-1 



1.12&2 



13B2 



Figure 6-4: Difference Chart for Lead-210 Set 9 



Grocery Store Data Analysis 



Lead-210 



The analyses on the grocery store data followed the same approach and 
methodology as that utilized to perform the analyses on the original FIPR data. Two 
radionuclides were considered: lead-210 and radium-226. In fact, like the original study, 



64 

this study counted the foods for two radionuclides: lead-210 and radium-226. The 
original study provided the data but no analysis on the polonium due to the lack of 
literature and values for the nonsampled food items and the concentration or dose that 
could be assigned to these values. A literature search did not turn up enough data to 
support analysis of this third radionuclide; therefore, similar to the original study, no 
analyses were performed in relation to it. 

Each variable is assigned a value. Intake data were obtained from a literature 
search of previous studies and databases on consumption in the United States. The 
concentration data for the various foods was obtained by experimental measurement 
discussed in the fourth chapter. Dose conversion factors were obtained from Federal 
Regulatory Guide # 1 1. All of these data were provided different distributions to obtain 
the nine sets of dose distributions and analyses. Table 6-8 shows the input to Crystal 
Ball. 

Table 6-9 illustrates the input variable and the output distributions obtained for 
the various sets tested. Table 6-10 shows the statistical output for the various sets. Figure 
6-5 is the forecast output of the Crystal Ball program for the 9 th set, and Figure 6-6 shows 
the difference between the programs best fit and the output data. 

Radium-226 

Table 6-1 1 illustrates the data input to the program to run the simulation and 
obtain results. Table 6-12 is the description of the distribution results. Table 6-13 shows 
the output statistics. Figure 6-7 is the frequency output for set 9, and Figure 6-8 is the 
difference comparison of this frequency output to the best fit distributions. 



65 



Table 6-8: Input Spreadsheet Data for Lead-210 Dose Calculation 



DCF 



5.40E-03 



(mrem/pCi) 



Diet Item 



Intake 



Concentration 
(pCi/kg) 



Intake 

(pCi/yr) 



Broccoli 



3.51 



829 



1062.07 



LEAFY 



Cabbage 


7.04 


858 


2204.72 


Collard Greens 


0.45 


1372 


225.35 


Lettuce 


23.38 


1237 


10556.19 


Mustard Greens 


0.45 


1622 


266.41 


Spinach 


3.28 


422 


505.22 


Turnip Greens 


0.45 


941 


154.56 



SEEDS/GRAINS 



Blackeyed Peas 


5.61 


494 


1011.54 


Rice 


22.94 


654 


5476.01 


Yellow Corn 


14.41 


506 


2661.38 



ROOTS 



Carrot 


2.92 


555 


591.52 


Onion 


4.19 


599 


916.08 


Radish 


0.32 


580 


67.74 


Turnip 


0.42 


401 


61.47 



GENERAL 



Cucumber 


2.62 


47082 


45024.52 


Green Beans 


8.80 


3837 


12324.44 


Green Peppers 


1.99 


431 


313.06 


Strawberries 


1.23 


715 


321.00 


Tomato 


25.18 


1011 


9291.80 


Watermelon 


3.44 


776 


974.35 


Squash/Zucchini 


1.26 


613 


281.92 


Totals 


133.89 




94291.34 


Total Diet 


3071.81 





Dose 



Non- Sampled 



9.07E+00 mrem/yr 



Sampled 



5.09E+02 mrem/yr 



Total 



5. 18E+02 mrem/yr 



66 



Table 6-9: Table of Input and Output Distributions for Lead-210 







Intake 


Concentration 


DCF 


Dose 


Set 


1 


LN 


LN 


LN 


LN 


Set 


2 


G 


LN 


LN 


Gamma 


Set 


3 


G 


G 


LN 


Gamma 


Set 


4 


G 


G 


G 


Gamma 


Set 


5 


LN 


G 


G 


Gamma 


Set 


6 


LN 


LN 


G 


Gamma 


Set 


7 


LN 


G 


LN 


LN 


Set 


8 


G 


LN 


G 


Gamma 


Set 


9 


LN 


LN 


LN 


LN 



Table 6-10: Statistical Comparison of Various Dose Rate Results Data for Lead-210 







Mean 


Std Dev 


Skewness 


Kurtosis 


COF 


Range 
Width 


Set 


1 


518 


63.9 


0.41 


3.26 


0.12 


563 


Set 


2 


518 


64.6 


0.36 


3.19 


0.12 


529 


Set 


3 


518 


64.2 


0.37 


3.23 


0.12 


541 


Set 


4 


518 


64.7 


0.2 


3.08 


0.12 


588 


Set 


5 


518 


63.9 


0.21 


3.12 


0.12 


541 


Set 


6 


517 


63.8 


0.22 


3.14 


0.12 


576 


Set 


7 


518 


64.6 


0.39 


3.26 


0.12 


529 


Set 


8 


518 


63.7 


0.21 


3.16 


0.12 


529 


Set 


9 


854 


1070 


6.02 


86.32 


1.27 


3150 



.CB3-T 



.00 
.023 
.00 
.ODD 



darby Chart 
frequency Comparison 






QCCBO 



1.QD&3 



20C&3 



3.CC&3 



Liyund Dstrbioi 

l\ten=&€&2 

SUDb/=1.07&3 



TcB 



4QC&3 



Figure 6-5: Set 9 Output and Distribution Fit for Pb-210 



67 



Overlay Chart 
Frequency Dfference 



COB 

.GDI 

.ODD 

-GDI 

-COB 





• 


:_j 


J 


J 1 lJlll.ll.1 .1. 1 - 1 In 1 




rrqi 


■ 1 1 1 II 1 ' 1 I ' 


1 



Lnjtmnd Darhijm 
M3an=84E&2 

sbCB/=i.a?&3 



Tea 



QdBO 



1.C0B-3 



2G0B3 



Figure 6-6: Difference Chart for Lead-210 Set 9 

Overall Analysis 
The above sets were each run with 20,000 trials each to decrease statistical error 
and improve comparability. The data show some very interesting results when compared 
to each other and then when compared to overall annual dose to an individual. 

Dose Data Comparison 

Lead-210 exhibited the highest dose in both the original set of data and the 
grocery store data. The original FIPR 1990 report data yielded a dose from 
ingestion of lead 210 of 21.4 mrem/yr for sets 1 through 8 and 34.7 mrem/yr 
for set 9. The grocery store data yielded a dose to the individual of 518 mrem/yr for 
sets 1 through 8 and 854 mrem/yr for set 9 individual of 877mrem/yr. The dose 
calculated from the grocery store data was 24 times higher than that calculated from the 
1990 FIPR data. 



68 



Table 6-11: Input Spreadsheet Data for Radium-226 Dose Calculation (Grocery Data) 



DCF 



1.30E-03 



(mrem/pCi) 



Diet Item 



Intake 



Concentration 



Intake 
(pCi/yr) 



Broccoli 



3.51 



5.00 



6.406 



LEAFY 



Cabbage 


7.04 


6.00 


15.418 


Collard Greens 


0.45 


6.00 


0.986 


Lettuce 


23.38 


4.00 


34.135 


Mustard Greens 


0.45 


17.00 


2.792 


Spinach 


3.28 


20.00 


23.944 


Turnip Greens 


0.45 


6.00 


0.986 



SEEDS/GRAINS 



Blackeyed Peas 


5.61 


3.00 


6.143 


Rice 


22.94 


2.00 


16.746 


Yellow Corn 


14.41 


6.00 


31.558 



ROOTS 



Carrot 


2.92 


4.00 


4.263 


Onion 


4.19 


4.00 


6.117 


Radish 


0.32 


4.00 


0.467 


Turnip 


0.42 


1177.00 


180.434 



GENERAL 



Cucumber 


2.62 


9.00 


8.607 


Green Beans 


8.80 


7.00 


22.484 


Green Peppers 


1.99 


4.00 


2.905 


Strawberries 


1.23 


4.00 


1.796 


Tomato 


25.18 


3.00 


27.572 


Watermelon 


3.44 


2.00 


2.511 


Squash/Zucchini 


1.26 


4.00 


1.840 


Totals 


133.89 




398.109 


Total Diet 


3071.81 





Dose 



Non-Sampled 



2.18E+00mrem/yr 



Sampled 



5.18E-01 mrem/yr 



Total 



2.70E+00 m/rem/yr 



69 



Table 6-12: Table of Input and Output Distributions for Radium-226 (Grocery Data) 







Intake 


Concentration 


DCF 


Dose 


Set 


1 


LN 


LN 


LN 


LN 


Set 


2 


G 


LN 


LN 


Gamma 


Set 


3 


G 


G 


LN 


Gamma 


Set 


4 


G 


G 


G 


Beta 


Set 


5 


LN 


G 


G 


Beta 


Set 


6 


LN 


LN 


G 


Beta 


Set 


7 


LN 


G 


LN 


Gamma 


Set 


8 


G 


LN 


G 


Beta 


Set 


9 


LN 


LN 


LN 


LN 



Table 6-13: Statistical Comparison 
(Grocery Data) 


Df Various Dose Rate Results Data for Radium-226 




Mean 


Std Dev 


Skewness 


Kurtosis 


COF 


Range 
Width 


Set 1 


2.7 


0.273 


0.31 


3.22 


0.1 


2.27 


Set 2 


2.7 


0.275 


0.31 


3.29 


0.1 


2.25 


Set 3 


2.7 


0.274 


0.31 


3.15 


0.1 


2.06 


Set 4 


2.7 


0.27 


0.02 


2.95 


0.1 


2.1 


Set 5 


2.7 


0.273 





2.95 


0.1 


2.21 


Set 6 


2.7 


0.272 


0.04 


3.03 


0.1 


2.16 


Set 7 


2.7 


0.271 


0.3 


3.21 


0.1 


2.45 


Set 8 


2.7 


0.272 


-0.01 


3.02 


0.1 


2.09 


Set 9 


4.38 


5.52 


5.6 


69.91 


1.28 


150 



.08 1 



Overlay Chart 
Freqjency Comparison 




Ixgrnrrd DstrfcUicn 

Wten=43EB0 

SHQy=55»0 



TcB 



QCC&O 



5CEB0 



1.GC&1 



1.SD-1 



2CC&1 



Figure 6-7: Set 9 Output and Distribution Fit for Radium-226 (Grocery Data) 



ODB 




-OB 



n 



Overlay Chart 
Frequency Dfferenoe 



'i " i JiWi ' h i ■ ^ ■ ' -■■ ' ■ - ■■ ■ ■ v- - ■' „ 



Tmrn 



I ■ 



(HBO 50BO 



IxgncirrEi Dsfirbiicn 

ltei=43E&0 
SaQy=55£K) 



Tea 



ia&i 



1.3E-1 



20CB-1 



Figure 6-8: Difference Chart for Radium-226 Set 9 (Grocery Data) 



70 



The dose from the grocery store data is believed to be higher for two reasons. The 
peak measured on the original analysis was the 40 KeV peak. The peak measured on the 
grocery store analysis was the 10.8 KeV peak. This peak was measured because of the 
successful recognition of this peak by the GammaVision program for this peak for the 
lead-210 radionuclide. This 10.8 KeV peak yielded a significantly higher correction 
factor than previously measured and observed for the alternate lead-210 peak. 

Radium-226 had the lowest dose per year of both radionuclides considered. The 
output from the analysis of the 1990 FIPR data yielded a dose to the individual from 
radium-226 of 5.91 mrem/yr for sets 1 through 8 and 9.56 for set 9. The grocery store 
data provided an individual dose that was lower than the FIPR data. The grocery store 
data dose to the individual was calculated to be 2.7 mrem/yr for sets 1-8 and 4.38 for set 
9. The dose calculated from the grocery store data was 45% of the dose calculated for the 
original FIPR dose calculation. 



71 

Comparing the dose to the individual from radium-226 and lead-2 1 from the 
FIPR data, it was calculated that dose from lead-2 10 was 3.6 times higher than the 
individuals dose from radium-226. A similar comparison of doses for the grocery store 
data concluded that the individual's dose attributable to lead-210 was 191 times greater 
than that attributable to radium-226 

Some of the differences between doses attributable to the radionuclides can be 
traced back to their reported dose conversion factors. Lead-210 is almost three times 
larger than radium-226. Consider this factor with the fact that lead-210 had some 
individual samples with high counts and a higher intersample comparison should be 
expected. 

Comparison of Distributions and Statistics 

The dose conversion factor distribution appears to have a strong effect on the dose 
distribution. A sensitivity analysis was performed on the various variables with the 
outcome determining that the dose conversion factor was over 10 times more sensitive to 
the output distribution that any other variable. The data reveal that multiplying three 
lognormal distribution yields a lognormal output distribution each time. Multiplying three 
normal distributions times each other provides a normal distribution for the output dose 
in two cases and a beta distribution in two other cases. Multiplying a mixture of 
lognormal distributions and normal distributions does not necessarily yield either of 
these distributions as an output. The best fit to the dose distribution output in the 
preceding case is illustrated above to be a lognormal, a normal, a beta, or a gamma 
distribution. 



72 

The beta distribution is a very flexible distribution commonly utilized to represent 
variability over a wide range (Decisioneering, 1996). This distribution can assume a wide 
variety of shapes when the values of alpha a beta are varied. 

The gamma distribution is related to the lognormal distribution and is used 
sometimes to represent pollutant concentrations and precipitation quantities. 

Set 9, in all four sets of analyses, was utilized to represent the most accurate 
quantity. The value of this dose in all four groups was significantly higher that the other 
eight sets in that group under consideration. The primary reason for this is the change in 
the dose conversion factor. Being the most sensitive variable and the large skewness 
introduced due to the determination of an accurate shape of this curve from a discussion 
with Dr. Eckerman, this provided an output dose distribution different from the other sets. 

Conclusions 

The purpose of this chapter was accomplished by a literature search that described 
the applicable and relevant literature to determine the committed effective dose 
equivalent, the term to describe the extended dose to an individual based on intake of a 
specific radionuclide. The data previously obtained were then analyzed with the original 
data and a comparison is provided. 

The shape of various dose distributions to individuals was determined for nine 
combinations of variable distributions in each of the two radionuclides in each of the two 
studies. The data from one study came from a previous 1990 FIPR report. The data for 
the other study were determined by experimental measurement from an earlier chapter in 
this series. The Crystal Ball program and monte carlo sampling method inherent to it 
were utilized to perform these analyses for each set of distributions. 



73 

The average individual annual dose, as stated in the introduction, is 360 mrem/yr. 
Lead-210 measurement is 518 mrem/yr for eight sets of analyses on grocery store 
samples and 854 mrem/yr for the most likely distribution scenario. The lead-210 dose to 
an individual from the analysis of the FIPR data was 34.7 mrem/yr for the case 9 and 
21 .4 mrem/yr for all others. The case 9 set of variable distributions is believed to be the 
most likely dose output. This output distribution is described by a lognormal distribution. 
Many reasons were observed for the higher value from the experimental data dose 
determination. A different peak measurement and a higher correction factor were both 
significant factors as well as the fact that the 10.8 KeV is at the lower edge of analysis for 
the system. In defense of a higher lead-210 dose, the original 1990 FIPR report chose not 
to use grocery store data due to the fact that only single replicates were being measured 
and the alternate fact that the dose obtained was 200 times greater than the other 
measurements. 

The radium-226 individual dose measurements for the case 9, the most likely 
case, also followed a lognormal distribution. The values of the dose to the individual 
were significantly lower than the lead-210 values. The dose for the FIPR data was 5.91 
mrem/yr for eight cases and 9.56 mrem/yr for the ninth and most likely case. The grocery 
store data provided a dose to the individual that measured 2.7 mrem/yr for 8 sets and 4.38 
mrem/yr for the most likely case. These data, compared to the 360 mrem/yr expected 
dose from natural sources, are less than 3% for all radium-226 measurements. 

The distributions described by the various analyses included normal, lognormal, 
beta, and gamma. The output, dose, and distributions were strongly influenced by the 
distribution assigned to the dose conversion factor variable. 



74 

This chapter is designed to determine a probabilistic dose to individuals from 
foods bought at local stores in Gainesville, Florida. The first chapter provided the 
introduction of a probabilistic dose approach. The second chapter described the literature 
search for the overall dissertation to determine the references that were used for each 
section. The third chapter determined the dietary intake values to be used and the most 
probable distribution to describe them. The fourth chapter described the actual 
experimentation performed to determine both the concentration of specific radionuclides 
in the various foods measured and the distribution to describe this concentration. The 
fifth chapter described the methodology to determine the dose conversion factor (DCF) 
value and distribution. The purpose of this chapter was to determine the value and 
distribution to describe the dose to an individual based on the values obtained in the 
previous chapters. The next and final chapter provides a conclusion and 
recommendations for future research in this area. 



CHAPTER 7 
CONCLUSIONS AND RECOMMENDATIONS 



This is the seventh and the last chapter intended to design and implement a 
methodology to determine a probabilistic radiation dose to individuals. This methodology 
is analyzed by application to data experimentally determined from foods bought at local 
stores in Gainesville, Florida. 

The first chapter in the series provided the introduction of a probabilistic dose 
approach. The explanation of how the current approach to individual dose determination 
was deterministic and resulted in a dose with a single number describing it. A 
probabilistic approach was explained and how this yielded a dose that was described with 
a distribution. 

The second chapter described the literature search for the overall dissertation to 
determine the references that were used for each section. This general literature search 
provided the basis for the background data utilized for the remainder of the dissertation. 

The third chapter determined the dietary intake values to be used and the most 
probable distribution to describe them. These values and data were derived from literary 
sources of previous studies and dietary surveys performed in the United States. 

The fourth chapter described the actual experimentation performed to determine 
both the concentration of specific radionuclides in the various foods measured and the 
distribution to describe this concentration. Samples from three different local stores were 
analyzed to determine concentrations of radium-226 and lead-210 in the foods. An 

75 



76 

additional study was performed to determine experimentally the type of distribution to 
describe best the concentration in foods. 

The fifth chapter described the methodology to determine the dose conversion 
factor (DCF) value and distribution. Literary sources as well as direct conversation with 
people at the cutting edge of dose conversion factor determination provided the data 
obtained in this chapter for the value and distributions to describe the dose conversion 
factor. 

The sixth chapter determined the value and distribution to describe the dose to an 
individual based on the values obtained in the previous chapters. The Crystal Ball 
program was utilized to perform groups of analyses on both original 1990 Florida 
Institute of Phosphate Research data as well as grocery store data. 

Crystal Ball is like any computer program. Good information in will yield good 
information out. The data that were measured had numerous data points that provided no 
counts at the specific peaks that were being observed. Minimum detectable activity 
numbers were input for these data points to provide for a large and, therefore 
conservative from a safety standpoint, dose estimate. The unsampled data points provided 
another source of error which was overcome by reference to previous work and data 
manipulation to provide a dose for these data points. This, however, provides another 
possible source for higher dose output. The Crystal Ball program provided an accurate 
way to sample the input to provide a distribution output that was as accurate as the input 
provided. 

The grocery store data showed a lognormal distribution for lead-210 with an 
average dose 854 mrem/yr for the most probable case and 518 mrem/yr for all other eight 



77 

cases. The FIPR data illustrated a lead-210 mean of 34.7 mrem/yr for the most probable 
case and 21 .4 consistently for all other cases. 

The reasons for such a high lead-210 dose is due to many factors: different peak 
counted, different calibration or correction factor, and the peak measured being at the 
lower edge of the detector's measurement limit. This number, as stated before, seems 
abnormally high and should be verified with other analyses. 

The grocery store radium-226 measurement for individual dose, by comparison, 
was 2.7 mrem/yr for eight cases and 4.38 mrem/yr for the ninth and most probable case. 
This value was lower than the individual dose value obtained from the data from the 1990 
FIPR report. This report yielded an individual dose of 5.91 mrem/yr for eight cases and 
9.56 mrem/yr for the most probable case. The most probable dose scenarios followed a 
lognormal distribution that closely approximated the dose conversion factor input 
distribution. 

The numbers for radium-226 are very similar to those obtained by FIPR in the 
1990 report and so support their data as well as extending the database. The lead-210 
measured in this report are consistent with the previous report in the fact that the lead-210 
general foods category radiation dose calculation from the grocery store samples ranged 
from 2 to 200 times higher than the literature value (Guidry et al., 1990). 

The methodology of using Crystal Ball and probabilistic dose calculation was 
successfully implemented in the previous chapter. The inclusion of distributions to 
account for fluctuations, errors and variations was very useful and provided a higher 
initial dose than the deterministic approach in the previous FIPR paper (Guidry et al., 
1990). The distribution groups allow for flexibility should future research determine more 



78 

accurate distributions for the variables. Additionally, the output distributions provide a 
visual aid for the public and researchers to understand radiation dose and the fact that it is 
a range and not just one number! 

Future analyses should, if possible, include the location of where samples are 
grown. Additional measurements should be taken to determine and confirm the normal 
distribution assigned to the food concentration. Additional Crystal Ball analysis should be 
performed on the calculational parameters and, therefore, the solution for the dose 
conversion factor formula. This would provide a more accurate distribution for the dose 
per unit intake factor. An analysis to determine the differences and advantages of the 
various dose conversion factors should be considered. A study should also be undertaken 
to determine the effect on changing the various distributions on the final dose. A 
determination should be made as to what may be the cause for the elevated measurements 
for lead-210. These are a few suggestions on the direction that this work should take in 
the future. 



APPENDIX A 
DATA SHEETS 



Item 


Store 


Weight 


Time Counted 


Detector 


File Saved 


Beef 


Publix 


556.6 


34187.1 


4 


beef.spc 


Beef Kidney 


Publix 


449.2 


86362.4 


4 


bfkid.spc 


Black-Eyed Peas 


Publix 


455.35 


86437.5 


2 


bleypeas 


Black-Eyed Peas 


Albertsons 


264.3 


72000 


2 


bepe.spc 


Black-Eyed Peas 


Winn Dixie 


473.8 


34098.9 


4 


bley3.spc 


Brazil Shells 


Publix 


304.2 


43149 


2 


bznutssh.spc 


Broccoli 


Publix 


267 


34167.9 


4 


brocclspc 


Broccoli 


Albertsons 


192.4 


71946.1 


2 


broc2.spc 


Broccoli 


Winn Dixie 


324.4 


34124.9 


2 


broc3.spc 


Cabbage 


Publix 


210.45 


34187.4 


2 


cabb.spc 


Cabbage 


Albertsons 


179.3 


34155.1 


4 


cabb2.spc 


Cabbage 


Winn Dixie 


214.15 


34122.6 


4 


cabb3.spc 


Carrots 


Publix 


286.9 


34187.8 


2 


carr.spc 


Carrots 


Albertsons 


421.1 


71940.8 


4 


carr2.spc 


Carrots 


Wnn Dixie 


365.9 


34061.3 


4 


carr3.spc 


Cauliflower 


Publix 


268.8 


34187.4 


4 


caul.spc 


Cauliflower 


Albertsons 


154.45 


34187.5 


2 


caul2.spc 


Cauliflower 


Winn Dixie 


396.1 


34167.7 


2 


caul3.spc 


Collard Greens 


Publix 


140.35 


34187.9 


4 


cogr.spc 


Collard Greens 


Albertsons 


421.15 


71940.8 


2 


cogr2.spc 


Collard Greens 


Wnn Dixie 


136.6 


34104.7 


2 


cogr3.spc 


Com 


Publix 


289.85 


34194.1 


2 


corn.spc 


Corn 


Albertsons 


199.6 


34187.3 


4 


corn2.spc 


Corn 


Wnn Dixie 


418.4 


34051.1 


4 


corn3.spc 


Cucumber 


Publix 


347.55 


34167.9 


2 


cuculspc 


Cucumber 


Albertsons 


257.6 


71942.7 


2 


cucu2.spc 


Cucumber 


Wnn Dixie 


324.2 


34087.2 


2 


cucu3.spc 


Eggplant 


Publix 


238.4 


34187.8 


2 


eggp.spc 


Eggplant 


Albertsons 


231.7 


71970.2 


4 


egpl2.spc 


Eggplant 


Wnn Dixie 


130.3 


34089 


2 


eggp3.spc 


Grapefruit 


Publix 


448.1 


34186.8 


4 


grap.spc 


Grapefruit 


Albertsons 


317.6 


71944 


4 


grap2.spc 


Grapefruit 


Wnn Dixie 


422.5 


34089 


4 


grap3.spc 



80 



81 



Item 


Store 


Weight 


Time Counted 


Detector 


File Saved 


Green Beans 


Publix 


216.7 


34186.9 


4 


grbr.spc 


Green Beans 


Albertsons 


250 


71971.9 


2 


grbe2.spc 


Green Beans 


Winn Dixie 


338 


34036.9 


2 


grbe3.spc 


Green Onions 


Publix 


97.2 


34187.8 


4 


gron.spc 


Green Onions 


Albertsons 


89.1 


71972.1 


4 


gron2.spc 


Green Onions 


Winn Dixie 


195.15 


34100.7 


2 


gron3.spc 


Green Peppers 


Publix 


321 


34186.9 


2 


grpe.spc 


Green Peppers 


Albertsons 


287.5 


71941.8 


4 


grpe2.spc 


Green Peppers 


Winn Dixie 


415.75 


34097.7 


4 


grpe3.spc 


Irish Creamer Potatoes 


Publix 


353.75 


34186 


4 


icp.spc 


Lemons 


Publix 


316.9 


43176.9 


4 


lem.spc 


Lemons 


Albertsons 


238.75 


71941.8 


2 


lemo2.spc 


Lemons 


Wnn Dixie 


372.7 


34154.8 


4 


lemo3.spc 


Lettuce 


Publix 


218.8 


43181.5 


2 


lettw.spc 


Lettuce 


Albertsons 


201.1 


71944 


2 


Iett2.spc 


Lettuce 


Wnn Dixie 


319.45 


34099.5 


2 


Iett3.spc 


Lima Beans 


Publix 


362.7 


43182.2 


2 


lima.spc 


Lima Beans 


Albertsons 


358.65 


71942.7 


4 


Iibe2.spc 


Lima Beans 


Wnn Dixie 


382.6 


34040.6 


2 


Iibe3.spc 


Mustard Greens 


Albertsons 


81.35 


34187.5 


4 


mugr.spc 


Okra 


Publix 


180.5 


34186 


2 


okra.spc 


Okra 


Albertsons 


240.5 


71970.2 


2 


okra2.spc 


Okra 


Wnn Dixie 


320.3 


34167.4 


4 


okra4.spc 


Onions 


Publix 


335.6 


43181.9 


2 


onio.spc 


Onions 


Albertsons 


323.15 


71979.8 


2 


onio2.spc 


Onions 


Wnn Dixie 


332.1 


34037.1 


4 


onio3.spc 


Oranges 


Publix 


446.9 


43176.9 


2 


oran.spc 


Oranges 


Albertsons 


381.3 


71973.3 


2 


oran2.spc 


Oranges 


Wnn Dixie 


379.6 


34030.4 


4 


oran3.spc 


Parsley 


Publix 


71.25 


43179.7 


4 


pars.spc 


Parsley 


Albertsons 


17.8 


34181 


2 


pars2.spc 


Parsley 


Wnn Dixie 


175.75 


34062 


2 


pars3.spc 



82 



Item 


Store 


Weight 


Time Counted 


Detector 


File Saved 


Peas 


Publix 


263.2 


43180.5 


2 


peas.spc 


Peas 


Albertsons 


289.35 


71970.9 


4 


peas2.spc 


Peas 


Winn Dixie 


342.6 


33922.1 


2 


peas3.spc 


Pole Beans 


Publix 


267.15 


34186.8 


2 


pb.spc 


Pole Beans 


Winn Dixie 


416.5 


34057.6 


4 


pobe3.spc 


Potato 


Publix 


398 


43179.7 


2 


pot.spc 


Potato 


Albertsons 


254.45 


86366.8 


2 


pot2.spc 


Potato 


Winn Dixie 


390.3 


34154.9 


2 


pot3.spc 


Purple Hull Peas 


Publix 


391.05 


43182.3 


4 


php.spc 


Purple Hull Peas 


Winn Dixie 


430.3 


34200 


2 


crpe3.spc 


Radishes 


Publix 


333.7 


34128.8 


4 


rad.spc 


Radishes 


Albertsons 


170.1 


71968.7 


4 


radi2.spc 


Radishes 


Winn Dixie 


310.3 


34100.9 


4 


rad3.spc 


Red Potatoes 


Publix 


348.15 


43182.2 


4 


rpotspc 


Red Potatoes 


Winn Dixie 


371.8 


34086.4 


4 


rpot3.spc 


Rice 


Publix 


518.55 


43182 


4 


rc.spc 


Rice 


Albertsons 


446.8 


71968.6 


2 


rice2.spc 


Rice 


Winn Dixie 


583.85 


34078.7 


2 


rice3.spc 


Spinach 


Publix 


99.85 


34185.9 


4 


sp.spc 


Spinach 


Albertsons 


69.3 


22702.8 


4 


spin2.spc 


Spinach 


Winn Dixie 


484.7 


34077.8 


4 


spin3.spc 


Strawberries 


Publix 


348.75 


34126.7 


2 


stra.spc 


Strawberries 


Albertsons 


278.5 


71973.3 


4 


straw2.spc 


Strawberries 


Winn Dixie 


337.1 


34051.8 


2 


straw3.spc 


Swiss Chard 


Publix 


173.65 


34187.1 


2 


swch.spc 


Tangerine 


Albertsons 


276 


34155.2 


2 


tan2.spc 


Tangerine 


Winn Dixie 


399.85 


34109.5 


4 


tan3.spc 


Tomatoes 


Publix 


358.8 


43181.4 


4 


tomat.spc 


Tomatoes 


Albertsons 


376.05 


34191.8 


2 


tom2w.spc 


Tomatoes 


Wnn Dixie 


434.4 


34048 


2 


5om3.spc 


Turnip Greens 


Publix 


135.65 


43183.1 


4 


tg.spc 


Turnip Greens 


Albertsons 


313.65 


34181.8 


4 


tugr2.spc 


Turnip Greens 


Winn Dixie 


564.2 


34185.4 


2 


tugr3.spc 



83 



Item 


Store 


Weight 


Time Counted 


Detector 


File Saved 


Turnip Root and Green 


Publix 


189.65 


34186 


2 


trag.spc 


Turnip Roots 


Publix 


275.1 


43148.7 


4 


turnroots.spc 


Turnip Roots 


Albertsons 


0.3 


71972.2 


2 


tum2.spc 


Watermelon 


Publix 


463.6 


43182.4 


2 


wm.spc 


Watermelon 


Albertsons 


396 


34187.4 


2 


wat2.spc 


Yellow Corn 


Publix 


324.6 


43182.1 


2 


yc.spc 


Yellow Corn 


Albertsons 


234.75 


34191.7 


4 


yc2.spc 


Yellow Corn 


Winn Dixie 


386.6 


34167.8 


2 


yeco3.spc 


Yellow Squash 


Publix 


331.6 


43183.1 


2 


yesq.spc 


Yellow Squash 


Albertsons 


219.4 


86366.8 


4 


yesq2.spc 


Yellow Squash 


Winn Dixie 


361.9 


33914.5 


4 


yellow3.spc 


Zucchini 


Publix 


394.3 


43180.5 


4 


zucc.spc 


Zucchini 


Albertsons 


256.4 


71971.9 


4 


zucc2.spc 


Zucchini 


Winn Dixie 


368.7 


34167.8 


4 


zucc3.spc 


Brazil Nuts 




226 


86369 


4 


bznuts.spc 



84 





Pb-210 Peaks 




Pb-210 


10.8 KeV 


Item 


Net (Counts) 


Error 


Beef 








Beef Kidney 


126 


47 


Black-Eyed Peas 








Black-Eyed Peas 








Black-Eyed Peas 






Brazil Shells 








Broccoli 








Broccoli 








Broccoli 








Cabbage 








Cabbage 








Cabbage 


45 


12 


Carrots 








Carrots 


91 


45 


Carrots 








Cauliflower 


105 


27 


Cauliflower 








Cauliflower 








Collard Greens 


43 


26 


Collard Greens 








Collard Greens 








Corn 








Corn 








Corn 








Cucumber 


4779 


142 


Cucumber 


182 


35 


Cucumber 








Eggplant 








Eggplant 








Eggplant 








Grapefruit 








Grapefruit 








Grapefruit 









85 





Pb-210 Peaks 




Pb-210 


10.8 KeV 


Item 


Net (Counts) 


Error 


Green Beans 


437 


59 


Green Beans 


211 


37 


Green Beans 








Green Onions 








Green Onions 








Green Onions 








Green Peppers 








Green Peppers 








Green Peppers 








Irish Creamer Potatoes 








Lemons 








Lemons 








Lemons 








Lettuce 








Lettuce 








Lettuce 








Lima Beans 


76 





Lima Beans 


76 


47 


Lima Beans 








Mustard Greens 


41 


29 


Okra 








Okra 








Okra 


28 


8 


Onions 








Onions 








Onions 








Oranges 








Oranges 


100 


38 


Oranges 








Parsley 








Parsley 








Parsley 









86 





Pb-210 Peaks 




Pb-210 


10.8 KeV 


Item 


Net (Counts) 


Error 


Peas 








Peas 


49 


44 


Peas 








Pole Beans 








Pole Beans 








Potato 








Potato 








Potato 








Purple Hull Peas 








Purple Hull Peas 








Radishes 


19 


30 


Radishes 


143 


43 


Radishes 


26 


7 


Red Potatoes 








Red Potatoes 


37 


12 


Rice 








Rice 


122 


39 


Rice 








Spinach 








Spinach 








Spinach 








Strawberries 








Strawberries 








Strawberries 








Swiss Chard 








Tangerine 








Tangerine 








Tomatoes 








Tomatoes 








Tomatoes 


87 


18 


Turnip Greens 


69 


33 


Turnip Greens 








Turnip Greens 


79 


20 



87 





Pb-210 Peaks 




Pb-210 


10.8 KeV 


Item 


Net (Counts) 


Error 


Turnip Root and Green 








Turnip Roots 


53 


33 


Turnip Roots 








Watermelon 








Watermelon 








Yellow Corn 








Yellow Corn 








Yellow Corn 








Yellow Squash 








Yellow Squash 


135 


44 


Yellow Squash 








Zucchini 








Zucchini 








Zucchini 








Brazil Nuts 


235 


86 



88 





Ra-226 Peaks 




Pb-214 


295 KeV 


Pb-214 


352 KeV 


Bi-214 


609 KeV 


Item 


Net (Counts) 


Error 


Net (Counts) 


Error 


Net (Counts) 


Error 


Beef 




















Beef Kidney 














271 


30 


Black-Eyed Peas 




















Black-Eyed Peas 




















Black-Eyed Peas 














Brazil Shells 


495 


42 


904 


43 


541 


31 


Broccoli 




















Broccoli 




















Broccoli 


39 


32 








69 


29 


Cabbage 




















Cabbage 


96 


32 


248 


30 


233 


22 


Cabbage 








82 


29 








Carrots 




















Carrots 


140 


44 


181 


42 








Carrots 














95 


20 


Cauliflower 




















Cauliflower 




















Cauliflower 




















Collard Greens 








81 


25 








Collard Greens 




















Collard Greens 




















Corn 




















Corn 




















Corn 




















Cucumber 




















Cucumber 


51 


31 














Cucumber 




















Eggplant 




















Eggplant 


75 


44 


271 


37 


237 


28 


Eggplant 




















Grapefruit 




















Grapefruit 





150 


39 











Grapefruit 








102 


26 


80 


23 



89 





Ra-226 Peaks 




Pb-214 


295 KeV 


Pb-214 


352 KeV 


Bi-214 


609 KeV 


Item 


Net (Counts) 


Error 


Net (Counts) 


Error 


Net (Counts) 


Error 


Green Beans 




















Green Beans 




















Green Beans 




















Green Onions 




















Green Onions 








227 


38 








Green Onions 




















Green Peppers 




















Green Peppers 








387 


411 


303 


30 


Green Peppers 




















Irish Creamer 
Potatoes 








37 











Lemons 











67 


27 





Lemons 




















Lemons 














6 


7 


Lettuce 




















Lettuce 




















Lettuce 





o - 














Lima Beans 








299 











Lima Beans 


180 


43 


299 


40 








Lima Beans 




















Mustard Greens 








189 


26 








Okra 




















Okra 




















Okra 




















Onions 




















Onions 




















Onions 




















Oranges 




















Oranges 




















Oranges 




















Parsley 








100 


29 








Parsley 




















Parsley 





















90 





Ra-226 Peaks 




Pb-214 


295 KeV 


Pb-214 


352 KeV 


Bi-214 


609 KeV 


Item 


Net (Counts) 


Error 


Net (Counts) 


Error 


Net (Counts) 


Error 


Peas 




















Peas 








163 


38 








Peas 




















Pole Beans 




















Pole Beans 








75 


24 








Potato 




















Potato 




















Potato 




















Purple Hull Peas 


66 


33 














Purple Hull Peas 




















Radishes 




















Radishes 








203 


37 


187 


27 


Radishes 




















Red Potatoes 




















Red Potatoes 




















Rice 




















Rice 




















Rice 




















Spinach 




















Spinach 




















Spinach 




















Strawberries 




















Strawberries 














242 


25 


Strawberries 




















Swiss Chard 




















Tangerine 




















Tangerine 














114 


15 


Tomatoes 














100 


20 


Tomatoes 




















Tomatoes 




















Turnip Greens 








156 


29 


104 


18 


Turnip Greens 




















Turnip Greens 





















91 





Ra-226 Peaks 




Pb-214 


295 KeV 


Pb-214 


352 KeV 


Bi-214 


609 KeV 


Item 


Net (Counts) 


Error 


Net (Counts) 


Error 


Net (Counts) 


Error 


Turnip Root and 
Green 




















Turnip Roots 


63 


33 














Turnip Roots 




















Watermelon 




















Watermelon 




















Yellow Corn 




















Yellow Corn 








159 


29 


126 


120 


Yellow Com 




















Yellow Squash 




















Yellow Squash 








145 


40 


183 


29 


Yellow Squash 


35 


24 














Zucchini 


32 


30 














Zucchini 




















Zucchini 




















Brazil Nuts 


4586 


167 


6936 


105 


4998 


83 



92 





Calibration 


Factors 


Bkgnd Count 


Minimum Det. Activity 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/cps) 


(pCi/cps) 


(counts) 


(counts) 


(pCi/g) 


(PCi/g) 


Beef 


1.10E+05 


1664 


0.000637 


0.0062 


7.63E-02 


3.60E-03 


Beef Kidney 


1.10E+05 


1664 


0.000637 


0.0062 


5.95E-02 


2.81 E-03 


Black-Eyed Peas 


3.40E+05 


1670 


0.0045 


0.0016 


4.82E-01 


1.41E-03 


Black-Eyed Peas 


3.40E+05 


1670 


0.0045 


0.0016 


9.10E-01 


2.67E-03 


Black-Eyed Peas 


1.10E+05 


1664 


0.000637 


0.0062 


8.98E-02 


4.24E-03 


Brazil Shells 


3.40E+05 


1670 


0.0045 


0.0016 


1 .02E+00 


2.99E-03 


Broccoli 


1.10E+05 


1664 


0.000637 


0.0062 


1.59E-01 


7.51 E-03 


Broccoli 


3.40E+05 


1670 


0.0045 


0.0016 


1 .25E+00 


3.66E-03 


Broccoli 


3.40E+05 


1670 


0.0045 


0.0016 


1.08E+00 


3.15E-03 


Cabbage 


3.40E+05 


1670 


0.0045 


0.0016 


1.66E+00 


4.86E-03 


Cabbage 


1.10E+05 


1664 


0.000637 


0.0062 


2.37E-01 


1.12E-02 


Cabbage 


1.10E+05 


1664 


0.000637 


0.0062 


1.99E-01 


9.37E-03 


Carrots 


3.40E+05 


1670 


0.0045 


0.0016 


1.22E+00 


3.56E-03 


Carrots 


1.10E+05 


1664 


0.000637 


0.0062 


6.96E-02 


3.28E-03 


Carrots 


1.10E+05 


1664 


0.000637 


0.0062 


1.16E-01 


5.49E-03 


Cauliflower 


1.10E+05 


1664 


0.000637 


0.0062 


1.58E-01 


7.46E-03 


Cauliflower 


3.40E+05 


1670 


0.0045 


0.0016 


2.26E+00 


6.62E-03 


Cauliflower 


3.40E+05 


1670 


0.0045 


0.0016 


8.82E-01 


2.58E-03 


Collard Greens 


1.10E+05 


1664 


0.000637 


0.0062 


3.03E-01 


1.43E-02 


Collard Greens 


3.40E+05 


1670 


0.0045 


0.0016 


5.71 E-01 


1.67E-03 


Collard Greens 


3.40E+05 


1670 


0.0045 


0.0016 


2.56E+00 


7.49E-03 


Corn 


3.40E+05 


1670 


0.0045 


0.0016 


1 .20E+00 


3.53E-03 


Corn 


1.10E+05 


1664 


0.000637 


0.0062 


2.13E-01 


1.00E-02 


Corn 


1.10E+05 


1664 


0.000637 


0.0062 


1.02E-01 


4.80E-03 


Cucumber 


3.40E+05 


1670 


0.0045 


0.0016 


1.00E+00 


2.94E-03 


Cucumber 


3.40E+05 


1670 


0.0045 


0.0016 


9.34E-01 


2.74E-03 


Cucumber 


3.40E+05 


1670 


0.0045 


0.0016 


1.08E+00 


3.16E-03 


Eggplant 


3.40E+05 


1670 


0.0045 


0.0016 


1.46E+00 


4.29E-03 


Eggplant 


1.10E+05 


1664 


0.000637 


0.0062 


1.26E-01 


5.97E-03 


Eggplant 


3.40E+05 


1670 


0.0045 


0.0016 


2.68E+00 


7.86E-03 


Grapefruit 


1.10E+05 


1664 


0.000637 


0.0062 


9.48E-02 


4.48E-03 


Grapefruit 


1.10E+05 


1664 


0.000637 


0.0062 


9.22E-02 


4.35E-03 


Grapefruit 


1.10E+05 


1664 


0.000637 


0.0062 


1.01 E-01 


4.75E-03 



93 



Item 



Green Beans 



Green Beans 



Green Beans 



Green Onions 



Green Onions 



Green Onions 



Green Peppers 



Green Peppers 



Calibration Factors 



Pb-210 



(pCi/cps) 



(pCi/cps) 



Green Peppers 



1.10E+05 



3.40E+05 



3.40E+05 



1.10E+05 



1.10E+05 



3.40E+05 



3.40E+05 



1.10E+05 



Ra-226 



1664 



1670 



1670 



1664 



1664 



1670 



1670 



1664 



1.10E+05 



1664 



Bkgnd Count 



Pb-210 



(counts) 



Ra-226 



(counts) 



0.000637 



0.0045 



0.0045 



0.000637 



0.000637 



0.0045 



0.0045 



0.000637 



0.000637 



0.0062 



0.0016 



0.0016 



0.0062 



0.0062 



0.0016 



0.0062 



Minimum Pet. Activity 



Pb-210 



(pcj'g) 



1.96E-01 



9.62E-01 



1.04E+00 



4.37E-01 



3.29E-01 



1.79E+00 



0.0016 1.09E+00 



0.0062 



1.02E-01 



1.02E-01 



Ra-226 



(pCi/g) 



9.25E-03 



2.82E-03 



3.03E-03 



2.06E-02 



1.55E-02 



5.25E-03 



3.19E-03 



4.81 E-03 



4.83E-03 



Irish Creamer 
Potatoes 



1.10E+05 



1664 



0.000637 



0.0062 



1.20E-01 



5.67E-03 



Lemons 



1.10E+05 



1664 



0.000637 



0.0062 



1.19E-01 



5.63E-03 



Lemons 



3.40E+05 



1670 



0.0045 



0.0016 



1.01E+00 



2.95E-03 



Lemons 



1.10E+05 



1664 



0.000637 



0.0062 



1.14E-01 



5.38E-03 



Lettuce 



3.40E+05 



1670 



0.0045 



0.0016 



1 .42E+00 



4.16E-03 



Lettuce 



3.40E+05 



1670 



0.0045 



0.0016 



1.20E+00 



3.50E-03 



Lettuce 



3.40E+05 



1670 



0.0045 



0.0016 



1 .09E+00 



3.20E-03 



Lima Beans 



3.40E+05 



1670 



0.0045 



0.0016 



8.56E-01 



2.51 E-03 



Lima Beans 



1.10E+05 



1664 



0.000637 



0.0062 



8.17E-02 



3.85E-03 



Lima Beans 



3.40E+05 



1670 



0.0045 



0.0016 



9.14E-01 



2.68E-03 



Mustard Greens 



1.10E+05 



1664 



0.000637 



0.0062 



5.22E-01 



2.47E-02 



Okra 



3.40E+05 



1670 



0.0045 



0.0016 



1 .93E+00 



5.66E-03 



Okra 



3.40E+05 



1670 



0.0045 



0.0016 



1.00E+00 



2.93E-03 



Okra 



1.10E+05 



1664 



0.000637 



0.0062 



1.33E-01 



6.26E-03 



Onions 



3.40E+05 



1670 



0.0045 



0.0016 



9.26E-01 



2.71 E-03 



Onions 



3.40E+05 



1670 



0.0045 



0.0016 



7.44E-01 



2.18E-03 



Onions 



1.10E+05 



1664 



0.000637 



0.0062 



1.28E-01 



6.05E-03 



Oranges 



3.40E+05 



1670 



0.0045 



0.0016 



6.95E-01 



2.04E-03 



Oranges 



3.40E+05 



1670 



0.0045 



0.0016 



6.31 E-01 



1.85E-03 



Oranges 



1.10E+05 



1664 



0.000637 



0.0062 



1.12E-01 



5.30E-03 



Parsley 



1.10E+05 



1664 



0.000637 



0.0062 



5.31 E-01 



2.50E-02 



Parsley 



3.40E+05 



1670 



0.0045 



0.0016 1.96E+01 



5.74E-02 



Parsley 



3.40E+05 



1670 



0.0045 



0.0016 



1.99E+00 



5.83E-03 



94 





Calibration Factors 


Bkgnd Count 


Minimum Det. Activity 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/cps) 


(pCi/cps) 


(counts) 


(counts) 


(pCi/g) 


(PCi/g) 


Peas 


3.40E+05 


1670 


0.0045 


0.0016 


1.18E+00 


3.46E-03 


Peas 


1.10E+05 


1664 


0.000637 


0.0062 


1.01E-01 


4.78E-03 


Peas 


3.40E+05 


1670 


0.0045 


0.0016 


1.02E+00 


3.00E-03 


Pole Beans 


3.40E+05 


1670 


0.0045 


0.0016 


1.31E+00 


3.83E-03 


Pole Beans 


1.10E+05 


1664 


0.000637 


0.0062 


1 .02E-01 


4.82E-03 


Potato 


3.40E+05 


1670 


0.0045 


0.0016 


7.80E-01 


2.29E-03 


Potato 


3.40E+05 


1670 


0.0045 


0.0016 


8.63E-01 


2.53E-03 


Potato 


3.40E+05 


1670 


0.0045 


0.0016 


8.95E-01 


2.62E-03 


Purple Hull Peas 


1.10E+05 


1664 


0.000637 


0.0062 


9.67E-02 


4.56E-03 


Purple Hull Peas 


3.40E+05 


1670 


0.0045 


0.0016 


8.11E-01 


2.38E-03 


Radishes 


1.10E+05 


1664 


0.000637 


0.0062 


1.27E-01 


6.01 E-03 


Radishes 


1.10E+05 


1664 


0.000637 


0.0062 


1.72E-01 


8.13E-03 


Radishes 


1.10E+05 


1664 


0.000637 


0.0062 


1.37E-01 


6.47E-03 


Red Potatoes 


1.10E+05 


1664 


0.000637 


0.0062 


1 .09E-01 


5.13E-03 


Red Potatoes 


1.10E+05 


1664 


0.000637 


0.0062 


1.14E-01 


5.40E-03 


Rice 


1.10E+05 


1664 


0.000637 


0.0062 


7.29E-02 


3.44E-03 


Rice 


3.40E+05 


1670 


0.0045 


0.0016 


5.39E-01 


1 58E-03 


Rice 


3.40E+05 


1670 


0.0045 


0.0016 


5.99E-01 


1.75E-03 


Spinach 


1.10E+05 


1664 


0.000637 


0.0062 


4.26E-01 


2.01 E-02 


Spinach 


1.10E+05 


1664 


0.000637 


0.0062 


7.52E-01 


3.55E-02 


Spinach 


1.10E+05 


1664 


0.000637 


0.0062 


8.78E-02 


4.14E-03 


Strawberries 


3.40E+05 


1670 


0.0045 


0.0016 


1.00E+00 


2.93E-03 


Strawberries 


1.10E+05 


1664 


0.000637 


0.0062 


1 .05E-01 


4.96E-03 


Strawberries 


3.40E+05 


1670 


0.0045 


0.0016 


1.04E+00 


3.04E-03 


Swiss Chard 


3.40E+05 


1670 


0.0045 


0.0016 


2.01 E+00 


5.89E-03 


Tangerine 


3.40E+05 


1670 


0.0045 


0.0016 


1.27E+00 


3.71 E-03 


Tangerine 


1.10E+05 


1664 


0.000637 


0.0062 


1 .06E-01 


5.02E-03 


Tomatoes 


1.10E+05 


1664 


0.000637 


0.0062 


1.05E-01 


4.97E-03 


Tomatoes 


3.40E+05 


1670 


0.0045 


0.0016 


9.28E-01 


2.72E-03 


Tomatoes 


3.40E+05 


1670 


0.0045 


0.0016 


8.05E-01 


2.36E-03 


Turnip Greens 


1.10E+05 


1664 


0.000637 


0.0062 


2.79E-01 


1.32E-02 


Turnip Greens 


1.10E+05 


1664 


0.000637 


0.0062 


1 .35E-01 


6.39E-03 


Turnip Greens 


3.40E+05 


1670 


0.0045 


0.0016 


6.19E-01 


1.81 E-03 



95 





Calibration Factors 


Bkgnd Count 


Minimum Det. Activity 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/cps) 


(pCi/cps) 


(counts) 


(counts) 


(pCi/g) 


(PCi/g) 


Turnip Root and 
Green 


3.40E+05 


1670 


0.0045 


0.0016 


1.84E+00 


5.39E-03 


Turnip Roots 


1.10E+05 


1664 


0.000637 


0.0062 


1.37E-01 


6.49E-03 


Turnip Roots 


3.40E+05 


1670 


0.0045 


0.0016 


8.02E+02 


2.35E+00 


Watermelon 


3.40E+05 


1670 


0.0045 


0.0016 


6.70E-01 


1.96E-03 


Watermelon 


3.40E+05 


1670 


0.0045 


0.0016 


8.82E-01 


2.58E-03 


Yellow Corn 


3.40E+05 


1670 


0.0045 


0.0016 


9.57E-01 


2.80E-03 


Yellow Corn 


1.10E+05 


1664 


0.000637 


0.0062 


1.81E-01 


8.54E-03 


Yellow Corn 


3.40E+05 


1670 


0.0045 


0.0016 


9.03E-01 


2.65E-03 


Yellow Squash 


3.40E+05 


1670 


0.0045 


0.0016 


9.37E-01 


2.74E-03 


Yellow Squash 


1.10E+05 


1664 


0.000637 


0.0062 


1.22E-01 


5.75E-03 


Yellow Squash 


1.10E+05 


1664 


0.000637 


0.0062 


1.18E-01 


5.56E-03 


Zucchini 


1.10E+05 


1664 


0.000637 


0.0062 


9.59E-02 


4.53E-03 


Zucchini 


1.10E+05 


1664 


0.000637 


0.0062 


1.14E-01 


5.39E-03 


Zucchini 


1.10E+05 


1664 


0.000637 


0.0062 


1.15E-01 


5.44E-03 


Brazil Nuts 


1.10E+05 


1664 


0.000637 


0.0062 


1.18E-01 


5.58E-03 



96 





Actual 


Reported 


Averages 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


Beef 


0.00E+00 


O.OOE+00 


0.076 


0.004 


0.076 


0.004 


Beef Kidney 


3.57E-01 


2.02E-03 


0.357 


0.002 


0.357 


0.002 


Black-Eyed Peas 


0.000 


0.000 


0.482 


0.001 


0.494 


0.003 


Black-Eyed Peas 


0.000 


0.000 


0.910 


0.003 


Black-Eyed Peas 


0.000 


0.000 


0.090 


0.004 


Brazil Shells 


0.000 


0.000 


1.021 


0.003 


1.021 


0.003 


Broccoli 


0.000 


0.000 


0.159 


0.008 


0.829 


0.005 


Broccoli 


0.000 


0.000 


1.251 


0.004 


Broccoli 


0.000 


0.000 


1.077 


0.003 


Cabbage 


0.000 


0.000 


1.659 


0.005 


0.858 


0.006 


Cabbage 


0.000 


0.000 


0.237 


0.011 


Cabbage 


0.677 


0.003 


0.677 


0.003 


Carrots 


0.000 


0.000 


1.217 


0.004 


0.555 


0.004 


Carrots 


0.330 


0.002 


0.330 


0.002 


Carrots 


0.000 


0.000 


0.116 


0.005 


Cauliflower 


1.257 


0.005 


1.257 


0.005 


1.466 


0.005 


Cauliflower 


0.000 


0.000 


2.260 


0.007 


Cauliflower 


0.000 


0.000 


0.882 


0.003 


Collard Greens 


0.986 


0.009 


0.986 


0.009 


1.372 


0.006 


Collard Greens 


0.000 


0.000 


0.571 


0.002 


Collard Greens 


0.000 


0.000 


2.559 


0.007 


Corn 


0.000 


0.000 


1.204 


0.004 


0.506 


0.006 


Corn 


0.000 


0.000 


0.213 


0.010 


Corn 


0.000 


0.000 


0.102 


0.005 


Cucumber 


136.830 


0.020 


136.830 


0.020 


47.082 


0.009 


Cucumber 


3.339 


0.003 


3.339 


0.003 


Cucumber 


0.000 


0.000 


1.078 


0.003 


Eggplant 


0.000 


0.000 


1.464 


0.004 


1.425 


0.006 


Eggplant 


0.000 


o.ooo 


0.126 


0.006 


Eggplant 


0.000 


0.000 


2.683 


0.008 


Grapefruit 


0.000 


0.000 


0.095 


0.004 


0.096 


0.005 


Grapefruit 


0.000 


0.000 


0.092 


0.004 


Grapefruit 


0.000 


0.000 


0.101 


0.005 



97 





Actual 


Reported 


Averages 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


Green Beans 


6.489 


0.013 


6.489 


0.013 


3.837 


0.007 


Green Beans 


3.987 


0.003 


3.987 


0.003 


Green Beans 


0.000 


0.000 


1.035 


0.003 


Green Onions 


0.000 


0.000 


0.437 


0.021 


0.852 


0.014 


Green Onions 


0.000 


0.000 


0.329 


0.016 


Green Onions 


0.000 


0.000 


1.791 


0.005 


Green Peppers 


0.000 


0.000 


1.088 


0.003 






Green Peppers 


0.000 


0.000 


0.102 


0.005 


Green Peppers 


0.000 


0.000 


0.102 


0.005 


0.430583 


0.004275 


Irish Creamer 
Potatoes 


0.000 


0.000 


0.120 


0.006 


0.120 


0.006 


Lemons 


0.000 


0.000 


0.119 


0.006 


0.414 


0.005 


Lemons 


0.000 


0.000 


1.008 


0.003 


Lemons 


0.000 


0.000 


0.114 


0.005 


Lettuce 


0.000 


0.000 


1.420 


0.004 


1.237 


0.004 


Lettuce 


0.000 


0.000 


1.197 


0.004 


Lettuce 


0.000 


0.000 


1.094 


0.003 


Lima Beans 


1.650 


0.000 


1.650 


0.003 


0.963 


0.003 


Lima Beans 


0.324 


0.003 


0.324 


0.003 


Lima Beans 


0.000 


0.000 


0.914 


0.003 


Mustard Greens 


1.622 


0.017 


1.622 


0.017 


1.622 


0.017 


Okra 


0.000 


0.000 


1.934 


0.006 


1.072 


0.003 


Okra 


0.000 


0.000 


1.000 


0.003 


Okra 


0.281 


0.001 


0.281 


0.001 


Onions 


0.000 


0.000 


0.926 


0.003 


0.599 


0.004 


Onions 


0.000 


0.000 


0.744 


0.002 


Onions 


0.000 


0.000 


0.128 


0.006 


Oranges 


0.000 


0.000 


0.695 


0.002 






Oranges 


1.239 


0.002 


1.239 


0.002 


Oranges 


0.000 


0.000 


0.112 


0.005 


0.682064 


0.003214 


Parsley 


0.000 


0.000 


0.531 


0.025 


7.378 


0.029 


Parsley 


0.000 


0.000 


19.614 


0.057 


Parsley 


0.000 


0.000 


1.990 


0.006 



98 





Actual 


Reported 


Averages 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


Peas 


0.000 


0.000 


1.180 


0.003 


0.821 


0.003 


Peas 


0.259 


0.004 


0.259 


0.004 


Peas 


0.000 


0.000 


1.023 


0.003 


Pole Beans 


0.000 


0.000 


1.307 


0.004 


0.704476 


0.004326 


Pole Beans 


0.000 


0.000 


0.102 


0.005 


Potato 


0.000 


0.000 


0.780 


0.002 


0.846 


0.002 


Potato 


0.000 


0.000 


0.863 


0.003 


Potato 


0.000 


0.000 


0.895 


0.003 


Purple Hull Peas 


0.000 


0.000 


0.097 


0.005 


0.453905 


0.003469 


Purple Hull Peas 


0.000 


0.000 


0.811 


0.002 


Radishes 


0.184 


0.004 


0.184 


0.004 


0.580 


0.004 


Radishes 


1.285 


0.006 


1.285 


0.006 


Radishes 


0.270 


0.001 


0.270 


0.001 


Red Potatoes 


0.000 


0.000 


0.109 


0.005 


0.214874 


0.00335 


Red Potatoes 


0.321 


0.002 


0.321 


0.002 


Rice 


0.000 


0.000 


0.073 


0.003 






Rice 


1.290 


0.002 


1.290 


0.002 


0.653919 


0.002407 


Rice 


0.000 


0.000 


0.599 


0.002 


Spinach 


0.000 


0.000 


0.426 


0.020 


0.422 


0.020 


Spinach 


0.000 


0.000 


0.752 


0.036 


Spinach 


0.000 


0.000 


0.088 


0.004 


Strawberries 


0.000 


0.000 


1.002 


0.003 


0.715 


0.004 


Strawberries 


0.000 


0.000 


0.105 


0.005 


Strawberries 


0.000 


0.000 


1.038 


0.003 


Swiss Chard 


0.000 


0.000 


2.010 


0.006 


2.010 


0.006 


Tangerine 


0.000 


0.000 


1.265 


0.004 


0.685906 


0.004364 


Tangerine 


0.000 


0.000 


0.106 


0.005 


Tomatoes 


0.000 


0.000 


0.105 


0.005 


1.011 


0.003 


Tomatoes 


0.000 


0.000 


0.928 


0.003 


Tomatoes 


1.999 


0.002 


1.999 


0.002 


Turnip Greens 


1.296 


0.009 


1.296 


0.009 


0.941 


0.006 


Turnip Greens 


0.000 


0.000 


0.135 


0.006 


Turnip Greens 


1.393 


0.002 


1.393 


0.002 



99 





Actual 


Reported 


Averages 




Pb-210 


Ra-226 


Pb-210 


Ra-226 


Pb-210 


Ra-226 


Item 


(pCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


(PCi/g) 


Turnip Root and 
Green 


0.000 


0.000 


1.841 


0.005 


1.841 


0.005 


Turnip Roots 


0.491 


0.005 


0.491 


0.005 


0.941 


0.006 


Turnip Roots 


0.000 


0.000 


801.988 


2.349 


Watermelon 


0.000 


0.000 


0.670 


0.002 


0.775771 


0.002272 


Watermelon 


0.000 


0.000 


0.882 


0.003 


Yellow Corn 


0.000 


0.000 


0.957 


0.003 


0.680 


0.005 


Yellow Corn 


0.000 


0.000 


0.181 


0.009 


Yellow Corn 


0.000 


0.000 


0.903 


0.003 


Yellow Squash 


0.000 


0.000 


0.937 


0.003 


0.613 


0.004 


Yellow Squash 


0.784 


0.004 


0.784 


0.004 


Yellow Squash 


0.000 


0.000 


0.118 


0.006 


Zucchini 


0.000 


0.000 


0.096 


0.005 


0.108 


0.005 


Zucchini 


0.000 


0.000 


0.114 


0.005 


Zucchini 


0.000 


0.000 


0.115 


0.005 


Brazil Nuts 


1.324 


0.007 


1.324 


0.007 


1.324 


0.007 



APPENDIX B 
CRYSTAL BALL OUTPUT DATA 



1990 FIPR Data 
Ra-226 

Setl 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.022 1 — 



Forecast Total 

Freqjency Chart 



.016 
.011 
.005 
.000 



221 Outliers 

439 



44030 




KB7 g 



59330 
rrrern^Br 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.92E+00 
5.89E+00 

6.23E-01 

3.88E-01 

0.3 

3.17 

0.11 

3.92E+00 

8.74E+00 

4.81 E+00 

4.41 E-03 



101 



102 



1990 FIPR Data 
Ra-226 

Setl 

Crystal Ball Output 

Distributions Fitting Chart 



.033 1 

.021 
.014 
.07 
.CCO 



40CBO 



O/erlay Chart 
Frequency Gbmparison 




5OB0 



60CBO 



7.0C&0 



LyuntJ □stritiiian 

Mhi=591&0 

SUQy=622&1 



Tea 



80C&0 



.003 

.002 

.ODD 

-0C2 

-£CB 



Overlay Chart 
Frequency Dfference 



■ 




■ 


. . Il I..I. Il.ll 


I, I. 


ll.l 


I llll. I I 


" ' - "Il I ' ■ «ll 


' 


ii'in p r i — 





Lyuiibl Dstrilxtiai 

Mhi=591&0 
StiCEy=6235-1 



Tcfel 



103 



1990 FIPR Data 
Ra-226 

Set 2 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.021 



forecast: Total 
Frequency Chart 



230 Outliers 

425 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.91 E+00 
5.88E+00 

6.30E-01 

3.97E-01 

0.32 

3.13 

0.11 

3.98E+00 

9.14E+00 

5.16E+00 

4.46E-03 



104 



1990 FIPR Data 
Ra-226 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



40CBO 



Overlay Chart 
Ft eqjency Comparison 




50CBO 



60CBO 



7.QBO 



Lpgnrrd DstrbJicn 

NfeBn=5SEB0 
SUQy=62&1 



TcH 



8CIB0 



.002 
GDI 

.000 
-071 
-02 



Overlay Chart 
Frequency Dff erence 



• 






■ 


... 1 Id 


,i\ 


1 


1. 


JLlljiIiI ii» i. 


■II PI'I 


II ■ 


II 


i ipi 


■h ■■■ 






■ 



UyuirtiDstrhiai 

Nfean=5£2B0 

SUQv=62E1 



TcH 



40DBO 



50C&O 



6CCB0 



7.0C&O 



aoceo 



105 



1990 FIPR Data 
Ra-226 

Set 3 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.CE3 1 — 



.017 
.011 
.006 
.ODD 



Forecast: Total 
Frequency Chart 




136 Outl ie is 
42 



431B0 



51©0 



60IB0 



S87BO 



339 



225 = 



113 





7.72BO 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.92E+00 
5.89E+00 

6.31 E-01 

3.99E-01 

0.3 

3.15 

0.11 

3.79E+00 

8.89E+00 

5.10E+00 

4.46E-03 



1 990 FIPR Data 
Ra-226 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



106 



4OB0 



Overlay Chart 
Freqjency Comparison 




5CDB0 



60CBO 



7.GCB0 



kyuiitJ Dstrtmcn 
l\fen=5SEB0 



Tea 



aODBO 



.003 1 




-OB 



Overlay Chart 
Frequency Dff erence 



■ 




.II . ,ll 


Jl, 


.i .iiiil.i. i, ... .. 


-■■ ■• ■ "II-- in™ "I' 


i |i-r |i|i - 


"i 1 1 1 | i ■ "i ■ ■ ■ i ■ 


• 


- 



LujuiidDstrhiicn 

Nfesn=5SB0 

9dQy=62S1 



TcB 



40CBO 5QBO 60EKD 



7.CCB0 aOBO 



107 



1 990 FIPR Data 
Ra-226 

Set 4 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.022 



Forecast: Total 

Frequency Chart 



tt)Cutiieis 

-1-432 




42EB0 



51CB0 



591B0 



672&0 



7SBB0 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.92E+00 
5.91 E+00 

6.29E-01 

3.95E-01 

0.06 

3.04 

0.11 

3.72E+00 

8.63E+00 

4.91 E+00 

4.45E-03 



108 



1990 FIPR Data 
Ra-226 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



40CBO 



Overlay Chart 
Frequency Cbmpariscn 




5GCBO 



7C0BO 



Mmd CMrtatoi 

IVbm=5SE&0 
&j[*v=6Z&1 



TcB 



accBO 



.02 T 



.001 

.ODD 

-C01 

-HE 



j-Mv 



Overlay Chart 
Frequency Dfference 



■ liilli 
|IT 



llll 



IF 



ill ill mi 



Jl_u 



I I 



Nond DdriUkn 

Wfeai=5£E&0 
SUCB/=62E-1 



TcH 



40C&0 50CBO 



60C&O 



7CC&0 acc&o 



109 



1990 FIPR Data 
Ra-226 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



20,000 Trials 
.022 ■ 



Forecast: Tota 1 
Frequency Chart 




201 Outliers 

441 



591B0 
rrrffn^ar 



33D7 



2205 = 



1102 



2 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.92E+00 
5.91 E+00 

6.27E-01 

3.93E-01 

0.05 

3.04 

0.11 

3.50E+00 

8.63E+00 

5.12E+00 

4.44E-03 



110 



1990 FIPR Data 
Ra-226 

Set 5 

Crystal Ball Output 

Frequency Chart 



4CCB0 



Overlay Chart 
Frequency Cbmpariscn 




5CCB0 



6OB0 



7CCB0 



BelaDaritita 
A0b=5OEB-1 
B=fcJ=66?&1 
Sde=1.3CE+1 



TcH 



aoc&o 



0C2 

1 " 
^ ctjd 

-D01 
-02 



Overlay Chart 
Frequency Dfference 



• 






■ 


. I.l.l.lll . 


| L L*J| 


M .MI 


1 


1 . ..... 


'■II III I'l'l 1 1 


IP 


II 


1 1 II "II ■ ■■ 1 -1 ' 











EBaDstribdiai 
Af*B=50&1 
BBa=6S&1 
S^e=1.3&-1 



TcB 



4OB0 



50C&O 



6CCB0 



7.0CBO 



aa&o 



Ill 



1 990 FIPR Data 
Ra-226 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



20,000 Trids 
.022 



Forecast: Total 
Frequency Chart 




43&0 



512B0 



59EBO 
mrar^ea' 



67&0 



7.5B0 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.92E+00 
5.92E+00 

6.26E-01 

3.91 E-01 

0.05 

2.97 

0.11 

3.51 E+00 

8.13E+00 

4.62E+00 

4.42E-03 



112 



1990 FIPR Data 
Ra-226 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



4OB0 



CX/erlay Chart 
Frequency GbmparJscn 




5CCB0 



60CBO 



70B0 



EBaDslribrticn 
ArtH=50?&1 
EBa=675B-1 
Stsle=1.3?&1 



TcH 



acr&o 



.ODBr 



.GDI 
ODD 

-jooi 

-JOB 



'■*■■■ L 



Overlay Chart 
Frequency Dfference 



i.. . I ■ lililll 

' r Tffl 



u 



-"-»! rn 1 1 i i 



EBaDstrihlicn 
A(te=507D-1 
Baa=672&1 
Sate=13EH 



TcB 



4CCB0 50C&0 6CCBO 70C&O 80CBO 



113 



1990 FIPR Data 
Ra-226 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



4QCB0 



O/erlay Chart 
Frequency Comparison 




5CCB0 



6CCB0 



7.CC&0 



NjntJ DstrfcLiai 
l\ten=5SE&0 



TcH 



aa&o 



.002 r 



.GDI 

.ODD 

-C01 

-as. 



Overlay Chart 
Frequency Dfference 



■ i-i . .Ih ■ _ I 



PIP 



UJ 



y_j 



■I l"|l " TTTf 



Istrrrd QstritUicn 

Hten=59E*0 

SHQv=62£1 



TcH 



4CCB0 



50&0 



60C&0 



7.0BO 



aoc&o 



114 



1 990 FIPR Data 
Ra-226 

Set 7 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.023 



Forecast: Total 
Frequency Chart 



•KJOtJiers 

451 




4Z&0 



SCB&O 



59IB0 
nieii'yea 



67SEH3 



E3 



7.SE&0 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.91 E+00 
5.88E+00 

6.24E-01 
3.89E-01 

0.32 
3.3 

0.11 
3.89E+00 
1.01E+01 
6.23E+00 
4.41 E-03 



115 



1 990 FIPR Data 
Ra-226 

Set 7 

Crystal Ball Output 

Distributions Fitting Chart 



4C0BO 



Overlay Chart 
Frequency Comparison 




5CTBO 



ifr&fl 



7.0CBO 



LcgnorrrEl Dslrfcubcn 

Nten=591B0 

SfciDEv=6261 



Tea 



aCEBO 



.QD2 




-02 



Overlay Chart 
Frequency Dfference 



• 




• 


... 1 III. , l\ 


. j_ 


,ll 


ilII j JjLJii Lij,. 


■ "|i r i ■ w 




i'iii|n|> | ■ 


1 





LcyuiitJ DslrbJicn 

r/fean=591&0 

3dDB/=63S1 



Tea 



4OB0 



50BO 



60B0 



7.0C&O 



80B0 



116 



1990 FIPR Data 
Ra-226 

Set 8 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.cei 



Forecast: Total 
Frequency Chart 




229 Cutlers 
427 



llUdbu, 



43S0 



51©0 



59©0 
msrlyeB 



673&0 



3232 

■ 

m 
K 

2B5 
KB7 





7.51B0 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.92E+00 
5.92E+00 

6.24E-01 

3.89E-01 

0.08 

3.04 

0.11 

3.67E+00 

8.95E+00 

5.28E+00 

4.41 E-03 



117 



1990 FIPR Data 
Ra-226 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



4OB0 



Overlay Chart 
Frequency Gbmpariscn 




50B0 



60B0 



7.GCB0 



BSaDsbriiilicn 
Afte=561EH 
Baa=94EEH 

SGte=1.S5&1 



TcH 



aoc&o 



.02 
GDI 

.ODD 
-GDI 

-CD2 



Overlay Chart 
Frequency Dfference 



-VMiW 



F 



LijiJil'iliu- 



||l I I ■"■! ■ ■ 



EaaDaribaicri 
Apte=561B-1 
EBa=94E&1 
Stzle=1.55EH 



Tea 



40C&O 50C&O 60CBO 



zccbo acr&o 



118 



1990 FIPR Data 
Ra-226 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



Overlay Chart 
Frequency Comparison 



m r 



.CED 

Si 

S .013 



.037 
.000 




kgnrrel Ddrbiicn 

Nfean=5S£&0 

SdC6/=632E1 



Tea 



4CCB0 



50B0 



600BO 



7.0B0 



acc&o 



119 



1990 FIPR Data 
Ra-226 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



.(27 1 



.(20 

: 013 
B 

■ 
.1 .007 



.QCO 



40CBO 



Overlay Chart 
frequency Ctmparison 




5CCB0 



6G0BO 



7.GCBO 



NjndDstribiJin 

l\fen=5SEB0 

3riCB/=S2e-1 



TcH 



aa&o 



.02 -r 



.001 

tit 

.ODD 
-001 

-02 



Overlay Chart 
Frequency Dfference 



■i l ,i. .ill 1 1 



i 



mr 



J 



i 



' fm 



■l llll ■■■■■" "' 



Njiibf DstrfaJim 

Ntei=5S&0 

ajD=v=62E1 



TcB 



1 1 p 1 i 

40C&O 5QB0 60CBO 70CBO 80CBO 



120 



1990 FIPR Data 
Ra-226 

Set 9 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.06 1 



Forecast: Total 
Frequency Chart 




SO Outliers 

SED 



■■•[■*■ — ■— 

3CEB-1 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
9.58E+00 
5.91 E+00 

1.20E+01 
1.46E+02 

5.08 
53.59 

1.26 

1.59E-01 

2.71 E+02 

2.70E+02 

8.55E-02 



121 



1990 FIPR Data 
Ra-226 

Set 9 

Crystal Ball Output 

Distributions Fitting Chart 



QCCBO 



Q/er lay Chart 
Freqjency Comparison 




1.12&1 



225B-1 



33E&1 



Lcgmral Dslrtiiicn 

Ktei=99&0 
SbDEv=121B-1 



Tea 



43&1 



.QDB 

.0D1 

.ODD 

-C01 

-OB 



Overlay Chart 
Frequency Dff erence 









'.„ 


ML., 


. Hi. i.i i ii. ..i .1.1 1 1. 


■ 1 


|m p. ■ 


ip 'i'tih ■■ iry'r 1 " ■ v 









Ixgu 1 1 y DsfrbUicn 

Nfean=95E+0 

SbDB/=121&-1 



TcH 



QCCBO 



1.12B-1 



22&1 



33E&1 



4SB-1 



122 



1990 FIPR Data 
Pb-210 

Setl 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.022 



.017 



.011 



.006 



cm 



Forecast Total 
Frequency Chart 



2M Outliers 

4G 



1.5&1 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.14E+01 
2.13E+01 

2.25E+00 

5.06E+00 

0.32 

3.18 

0.11 

1.45E+01 

3.22E+01 

1.76E+01 

1.59E-02 



123 



1990 FIPR Data 
Pb-210 

Setl 

Crystal Ball Output 

Distributions Fitting Chart 



CE7 

.(23 
.013 
.CD7 
.COO 



1.4&1 



Overlay Chart 
Frequency Comparison 






kgrnrrd DsbibiJcn 

Mhv=21«H 

SdDB/=22EKD 



TcB 



1.75B-1 



2t&1 



2€&1 



23&1 



.CQ2 




-02 



Overlay Chart 
Frequency Dfference 



■ 






■ 


, 


,l l,l 


, u 


li. i . 1 , 1 1 1 , . . 


■ ""■■ -lllll - ■ ■ 




IT 


i i ii i h | ■'-'"■ i i" 


■ 





L ujund Dslnbicn 
l\fen=2-^&1 

SUC&/=22EK) 



TcB 



1.4&1 



1.7SB-1 2t&1 



24E&1 



28C&-1 



124 



1990 FIPR Data 
Pb-210 

Set 2 

Crystal Ball Output 

Frequency Chart 



20,000 Trids 
.021 1 — 



1 .011 

s 

IS .CDS 
ODD 



Forecast Total 
Frequency Chart 



tSEM 




200 Cutlers 
427 



2202 



2135 



1057 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.14E+01 
2.13E+01 

2.25E+00 

5.06E+00 

0.29 

3.1 

0.11 

1.42E+01 

3.24E+01 

1.82E+01 

1.59E-02 



125 



1 990 FIPR Data 
Pb-210 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



.035 
.019 
.013 
.OB 
.000 



14B-1 



Overlay Chart 
Frequency Comparison 




1.7BB-1 



2XEM 



24EB-1 



LflonoiTSl Dstritutian 

l\ten=21<&1 

SfcJC&/=22©0 



Tea 



28C&-1 



.002 1 



.001 

.000 

-001 

-002 



Overlay Chart 
Frequency Dfference 



- 


• 


..II fall. 


■J,„.ll, 


JW 


I.I.. ... .11 


"IIHIIII 


'"' 1 


III' II 1 ' 1 











IficronTEl QstritUicn 

lvfan=21€H 

SdC6/=22EB0 



Tea 



1.4B-1 



I7E&1 



21C&1 24E&-1 



28C&-1 



126 



1990 FIPR Data 
Pb-210 

Set 3 

Crystal Ball Output 

Frequency Chart 



20,000 Trids 

.GE2 -I — 



Forecast: Total 
Frequency Chart 



Z6 Cutlers 

441 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.13E+01 
2.12E+01 

2.26E+00 

5.09E+00 

0.37 

3.27 

0.11 

1.38E+01 

3.35E+01 

1.96E+01 

1.59E-02 



127 



1990 FIPR Data 
Pb-210 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



m 



s m 




5 .013 


E 


■ 


|g 


il .07 


■■ 


ODD 



1.4CB-1 



Overlay Chart 

Frequency Comparison 






1.75B-1 



2t&1 



2«f1 



LyuiitJ DstnQJjcn 

Mhi=213&-1 

SUC&/=22E&0 



TcH 



2SB-1 



QD2 t 
.001 

.ODD 
-CD1 
-0Q2 



CVer lay Chart 
Frequency Dff erence 













- 




. .I..II . .1, 


1 


1 






A 


jj 


K*a 


.il 1 ml i . i 




' ' III '1 1 


II 


"1 




,|i,- 


M I ii ■■. 















Uxjuii tl DstitUiai 

Nbn=2t&1 

SbC&/=22E*0 



Tea 



1.4B-1 



17E&-1 21C&1 



24&1 



280E+-1 



128 



1990 FIPR Data 
Pb-210 

Set 4 

Crystal Ball Output 

Frequency Chart 



20,000 Trids 
.022 



R " 



.011 
.CCB 
.ODD 



Forecast: Total 
Frequency Chart 



238 Outliers 

437 



1SB-1 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.13E+01 
2.13E+01 

2.25E+00 

5.08E+00 

0.06 

3.04 

0.11 

1.21 E+01 

3.05E+01 

1.84E+01 

1.59E-02 



129 



1990 FIPR Data 
Pb-210 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



m 1 

.cm 

.014 
.QDT 

.ODD 



1.4&1 



O/erlay Chart 
Frequency Gbmparisan 




BaaDsfribiicn 
Apte=51»-1 
Baa=7t&1 
Sc~le=50E&-1 



TcB 



17&1 



21C&1 



24EM 



28C&1 



.GCB 




-OB 



Overlay Chart 
Frequency Dfference 







.... 1 1 .1 lll.lll 1 . 1. 


U 


1 ii l 


till 


■Li i.i. 


II 1 1 ■ 1 lj 1 


r 


T 


||| 1' II Hl|l ■■ 


■ 




• 



ESaDstritiim 
Afte=516B-1 
B=fca=712&1 
Stde=5C6&1 



Tea 



-L4&1 



17SEH 



2KD-1 



24&1 



2S&1 



130 



1990 FIPR Data 
Pb-210 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



CED 
.014 
.007 

.ODD 



1.4CD-1 



O/erlay Chart 
Frequency Cbmparison 






Nrtrt DdritUicn 
Mar=213B-1 

&JCEv=22&0 



Tea 



17&1 



21C&-1 



24&1 



2S&1 



GCB 




-CD3 



Overlay Chart 
Frequency Dfference 









... im 1 1. .1 it...!, i I 


1 il 


Jllt- 


Jk 


in ... 


ii- 1 1 1| | 


"1 


i 


lli " II Fiji'' 


• 









Hjrri DstritUicn 

Mhi=2"EB-1 

3dQv=22©0 



TcB 



1.4B-1 



1.7&1 



21CB-1 24&1 



23&1 



131 



1990 FIPR Data 
Pb-210 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



.m 
1 " 

.OM 

.007 
CEO 



14B-1 



O/erlay Chart 
Frequency Comparison 



illfc 


A I III 


■ 


4 




- ^^lllll 


llfenrrn^ 



UrpnTTd DstibJiai 

Mam=2"EB-1 

St!Da/=22&0 



Tea 



175EH 



21C&1 



24&-1 



28C&1 



.004 1 



.02 

.cm 

-02 
-CM 



Overlay Chart 
Frequency Off erence 







■ 


. .ml 


ll. 


II 




i.i i 1 ii. 


■ in nijiiri'ii 1 i 


i 


1 


p 


ii|'|'| ■•■ 


■ 




• 



Lxparrt DstribLticn 

Msn=212B-1 

aiQy=2ZEtO 



Tea 



14B-1 



17S-1 



2t&1 



2ffiH 



23B-1 



132 



1990 FIPR Data 
Pb-210 

Set 5 

Crystal Ball Output 

Frequency Chart 



20,000 Trids 
.GE2 1 



Forecast Total 
Frequency Chart 



221 Outliers 

439 




217&1 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.14E+01 
2.13E+01 

2.27E+00 

5.15E+00 

0.05 

3.06 

0.11 

1.22E+01 

3.12E+01 

1.90E+01 

1.60E-02 



133 



1990 FIPR Data 
Pb-210 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



O/eriay Chart 
Frequency Cbmpar tson 




BetaDslrihiiai 
AftB=5d&1 
Baa=673&1 
ade=50B-1 



ToB 



14EH 



17&1 



2KB-1 



24EB-1 



28QB-1 



.GC2 




-JX2 



Overlay Chart 
Frequency Dfference 



■ 










• 


,,h 


1 


ill ,. 


1 1 


X. 






ii ,. 


■ "''I'l'lll 1 1 ' ' II ■ II 1 1 


1 


r 


■I 


if 


ni ii ■■ 


- 








■ 



KaQstritUiai 
Af*B=5Q&1 
Baa=672&1 
ade=5CC&-1 



TcH 



1.4B-1 



17SEH 



2K&1 



249&1 



28&1 



134 



1990 FIPR Data 
Pb-210 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



140EH 



Orerlay Chart 
Frequency CbmparisGn 




17SEH 



2X&-1 



24&1 



Nrrrel Qstrihlicn 

l\ten=214&1 

3dDEv=22/B0 



Tea 



28CEH 



.OB 

0D1 

Si 

.ODD 
-C01 
-OB 



Oeri ay Chart 

Frequency Dfference 



• 








■ 


. . l.-lll 1 


1 


km 




In. 


I , 




ll 1 ., 


■l|||l 1 •■)• | 


r 


■ii 




I| "|l I'l 


., |.|| -.,", , | 


■ 






■ 



NonmEl DdritUicn 

Man=21<&1 

3dDB/=22?&0 



TcH 



1.4&1 



175&-1 2X&1 



24&1 



2SB-1 



1990 FIPR Data 
Pb-210 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



135 



.CBB 

.019 
JOB 

.006 
.ODD 



1.4B-1 



Overlay Chart 

Frequency Cbmpar ison 



aMl 


/111 


||l 


« 




jTh*. 


- ... IJ ^I1IIII 




lllllllllllinTiTTrirrrrrTr^T 



Uyunil Dstnbicn 
Mhi=21-&-1 

&JDB/=23C&0 



Tea 



17SB-1 



2K&1 



24&1 



28C&1 



.QD3 1 



.001 

.ODD 

-C01 
-OB 



Overlay Chart 
Frequency Dff erence 









1 II 


1 1 . ll 1 ll 1 1 1 ,.l 1 .ill I.I.I 


■'■iii|'|||'i|ii"iV' I. i| 


I 


llll"'l 


• 


■^jff 





Ixy und Dslnbiiicn 

l\fen=21<&-1 

SBC&/=23CBO 



TcH 



1.4B-1 



17EEH 2K&1 



24&1 



28&1 



136 



1990 FIPR Data 
Pb-210 

Set 6 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.CE2 



Forecast: Total 
Frequency Chart 




B5 Cutlers 

433 



3292 



- 2195 C= 



KB7 B 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.13E+01 
2.13E+01 

2.28E+00 

5.18E+00 

0.08 

2.99 

0.11 

1.24E+01 

3.14E+01 

1.90E+01 

1.61E-02 



137 



1990 FIPR Data 
Pb-210 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



MOEM 



Overlay Chart 
Frequency Gbmpariscn 




175EH 



2KB-1 



24&1 



Nfcrrrel Dslrititicn 

l\ten=213B-1 

3dC©/=22BB0 



TaB 



28D-1 



Overlay Chart 

Frequency Qfference 



.CCB - 






" 




.ODD - 

-flE - 

mo . 




, 


rV 


„.Jj 


I ihl.i mi .i 






pir 


T[ 


"in 




T| 1 '"| 


■ 







Nxn^ Qs&ibiicn 

Ntean=212B-1 

3riCEv=22E&0 



TcH 



MEM 



1.7E&1 



2KB-1 



24&1 



260&1 



138 



1990 FIPR Data 
Pb-210 

Set 7 

Ciystal Ball Output 

Frequency Chart 



20,000 Trials 
.CG3 1 



Forecast: Total 
Frequency Chart 



-B7 Outliers 
451 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.14E+01 
2.13E+01 

2.26E+00 

5.09E+00 

0.33 

3.18 

0.11 

1.36E+01 

3.18E+01 

1.82E+01 

1.59E-02 



139 



1990 FIPR Data 
Pb-210 

Set 7 

Crystal Ball Output 

Distributions Fitting Chart 



.027 
.CEO 
.013 

.CCf 
COD 



1.4&1 



CVerlay Chart 
Frequency Qxnpartson 




17S-1 



2KB-1 



24E&1 



Lnjumd DstritUian 
IVten=21<&1 

3dCB/=22&0 



TcB 



28CB-1 



.002 
.001 
.ODD 

-£01 
-£02 



CX*rlay Chart 
Frequency Dfference 



■ 


■ 


... Jl llll . .1 1. 


i. ii. 


jl i. 


ll'| i|'HI Mil 


1 1 ■ 


1 "l fnir ' 


■ 




■ 



L uju ii hl Dstrituticri 
Mehi=2"1&1 

StiGv=22&0 



Tea 



1.4B-1 



17EH 



21C&-1 



24&1 



23CB-1 



140 



1990 FIPR Data 
Pb-210 

Set 8 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.022 



forecast: Total 
Frequency Chart 



2)8 Outliers 

n-447 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
2.14E+01 
2.14E+01 

2.28E+00 

5.18E+00 

0.07 

3.05 

0.11 

1.20E+01 

3.02E+01 

1.81E+01 

1.61E-02 



141 



1990 FIPR Data 
Pb-210 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



1.4&1 



Overlay Chart 
Frequency Cbmpariscn 




17E&I 



2K&1 



24&1 



EaaDaritmcn 
Afte=531&1 
Bfc=812EH 
Szie=54»-1 



TcH 



28C&1 



.ODB 

.GDI 

.ODD 

-D01 

-OB 



Overlay Chart 
Frequency Dfference 



■ 






■ 


1 .1 .1 1 1 .. 1 1 1 1 


1 II 


■J 


jj,u 


M i .ii i ii. ■ 


■I]! l"""l l"l" l"l"l" l"l ■ 


[1 '1 


PI 


i| - «|-| -■ r ■■!■ 


■ 







BJaDstritiiicr) 
AftH=531&-1 
ffia=81£H 
Sde=54&1 



Tea 



"L4&1 



175EM 



21CB-1 



24&1 



23B-1 



142 



1990 FIPR Data 
Pb-210 

Set 9 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.06 



forecast: Total 
Frequency Chart 




940uUiers 
— r sob 



lllfulilllilil; 



681 
227 



1.09&2 



-7 

14E&2 



)> 



Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
3.47E+01 
2.14E+01 

4.35E+01 

1.89E+03 

5.18 

56.66 

1.25 

3.96E-01 

9.65E+02 

9.65E+02 

3.08E-01 



90FIPRData 
Pb-210 

Set 9 

Crystal Ball Output 

Distributions Fitting Chart 



143 



QdBO 



Overlay Chart 

Fre qjency Com par i son 




37EB-1 



7SD-1 



1.t&2 



Injnmd Dsfrbiicn 

H/fem=347&1 

SbCB/=43S&1 



TcH 



1.SCB2 



.003 f 



.001 

.000 
-£D1 
-OB 



71 



Overlay Chart 

Frequency Off erence 



llllll, .1 J.ll.,1 



!■■ .1 



ii »■ » ■■■■■'■■■.,' ■ . 



ii ||| | I'll" ■■ pmnr'T n v * 



UjgrrTTEl DslrbJicn 
NfeBn=347&1 

SUCB/=43G&-1 



TcB 



Q0C&O 



37E&1 



7.SD-1 



1.12B2 



ISDB2 



144 



Grocery Store Data 
Ra-226 

Setl 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.CE2 



Fbrecast: Total 
Frequency Chart 




213 Outliers 
46 



3315 

223 
1115 





341B0 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.69E+00 


Mode 


— 


Standard Deviation 


2.73E-01 


Variance 


7.44E-02 


Skewness 


0.31 


Kurtosis 


3.22 


Coeff. of Variability 


0.1 


Range Minimum 


1.78E+00 


Range Maximum 


4.06E+00 


Range Width 


2.27E+00 


Mean Std. Error 


1.93E-03 



145 



Grocery Store Data 
Ra-226 

Setl 

Crystal Ball Output 

Distributions Fitting Chart 



.CBB 

.021 
.014 
.07 
ODD 



17EK) 



Oerlay Chart 
Frequency Comparison 




21SB0 



263BO 



30B0 



LyuntJ DstnbJicn 
Nten=27C&0 

SbD=v=27E-1 



TcH 



33B0 



ODB 1 



.GDI 

.ODD 
-CD1 

-OB 



Overlay Chart 
Frequency Dfference 





■ 


. . , ll.llll 


,', 1 J 


,i il III. I.I .1.. 1... 


"Ml 1 


■|p 


'1 ' 


■j ■v™ 


III- | |M" | |i 


■ 






■ 



IxyuntJ Dslritiiiai 

l\ten=27TJBO 

StJD3/=273&1 



TcH 



146 



Grocery Store Data 
Ra-226 

Set 2 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.CB3 1 



Forecast: Total 
Frequency Chart 




214 Outliers 
462 



3C5 

■ 

231 = 

i 

1155 g 




27CBO 
rrrarr^ea' 



34B0 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.69E+00 


Mode 


— 


Standard Deviation 


2.75E-01 


Variance 


7.56E-02 


Skewness 


0.32 


Kurtosis 


3.29 


Coeff. of Variability 


0.1 


Range Minimum 


1.88E+00 


Range Maximum 


4.13E+00 


Range Width 


2.25E+00 


Mean Std. Error 


1.94E-03 



147 



Grocery Store Data 
Ra-226 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



CX/erlay Chart 
Frequency Cbmpari son 




G&TmaDstribiicn 

Lx=a6?&i 

Sde=411&2 
9*pe=447&1 



ToH 



175BO 



21EK) 



26EBO 



30E&O 



3SB0 



148 



Grocery Store Data 
Ra-226 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



CB3 -r 

.(21 
.OM 
.07 
ODD 



17»0 



CVerlay Chart 
Frequency Ccmparrscn 




219&0 



263BO 



30SO 



Nbrrd Dstrbiiai 

M=m=2XD0 

SfclDEy=27S&1 



Tea 



33B0 



.OBI 




-OB 



Overlay Chart 
Frequency Dfference 



ill 


1 




....I..IIIIIIIII.I llll.. ..1 


J" 


1, 


Li . 


1 If ■ 


r 


|,| ■ , -,.|||'..,.||. 


■ 


■• ~1 


• 



Njtt^ Dstrfaiicn 
M3an=2XB0 

SUC&/=275&1 



TcB 



175BO 21SB0 



26&0 



30&0 39B0 



149 



Grocery Store Data 
Ra-226 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



m 




: .014 


s 


M 


« 


il .007 


"™ 


.arj 



17»0 



Overlay Chart 
Frequency Comparison 




2-BBO 



LojuiTd Dsrfaiai 

l\fen=27E&0 

SUCB/=27E&1 



Tea 



3SD&0 



cm 1 



001 

.coo 
-coi 

-CCB 



Overlay Chart 

Frequency Dff erence 



•■ ■ ■ i 



■ Yp ' 



J1U 



hr 



JiLu 



I' I ■! 



"i rii r "f 



17EB0 



21G&0 



26EBO 



30EBO 



Ixyunbi Darblon 

Mbi=27C&o 

SHD3/=27SE1 



Tea 



3S&0 



150 



Grocery Store Data 
Ra-226 

Set 3 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.CE3 1 



.017 
.012 
QD3 
GOD 



Forecast Total 
Frequency Chart 




164 Cutlers 

-r4BD 



20EBO 



241B0 



277B0 
rrram^ar 



31-&0 



3505*0 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.69E+00 


Mode 


— 


Standard Deviation 


2.74E-01 


Variance 


7.49E-02 


Skewness 


0.31 


Kurtosis 


3.15 


Coeff. of Variability 


0.1 


Range Minimum 


1.87E+00 


Range Maximum 


3.93E+00 


Range Width 


2.06E+00 


Mean Std. Error 


1.94E-03 



151 



Grocery Store Data 
Ra-226 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



17E*0 



Overlay Chart 
Frequency Comparison 




21SB0 



2SB0 



3GEK) 



G&riTBDslribiiai 
Loc=Q4BE-1 

Sae=42EE2 

9^e=414Ef1 



Tea 



35DBO 



.CDB 
JDDI 

.ceo 
-mi 

-OB 



Overlay Chart 
Frequency Dfference 





■ 


. . II III, 1 J 


.,.1 


,.l,l 


il .. .1. h... 


' • ■ '1 II'HI 


M 1 


T 


|'M||| III' 1" 


■ 






■ 



GkTTTBDstribdiai 

Le=94EE-1 

Scde=42E2 



Tea 



175B0 



21SBO 



262BO 



3G&0 



3SBO 



152 



Grocery Store Data 
Ra-226 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



.(03 
.00 

.014 
.07 

.015 



1.7EKD 



Overlay Chart 
frequency Cbmpariscn 




2WB0 



262B0 



306BO 



Nfcrrr^ DstrtLBcn 

l\ten=27CBO 

SdQv=27S1 



Tea 



33B0 



.OB 

.GDI 

.000 

-C01 

-DOB 



Overlay Chart 
Frequency □fference 



• 


lllli 


.„,,.<fljl III 1 , 


1 II 


,111, 


Ill ,1. . 


■ r 


1" 








■> ill 1 "!*' 


■ 


'1 


'1 







NjtteI DjjrtUkn 

Ma£n=27CBO 
SUD3/=274&1 



Tea 



1.7EK) 21SB0 25B0 30BO 3SB0 



153 



Grocery Store Data 
Ra-226 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



.CEB 



.021 



.014 



.ay 



Overlay Chart 
Frequency Comparison 



.coo J — i * 

17SB0 2-KBO 




26EB0 



30EBO 



Iflgnnti DslrtUicn 

IYtei=2vT£tO 

SUC&/=274&1 



TcB 



33B0 



QD2 




-02 



Overlay Chart 
Frequency Dfference 



■ 


' 


II 1.1 


I 


1 nil 


1 n 1. 1 1. , J. 1 i..i. 




WW 


Tr 




. -||| ™ i 


• 









Uyunti DsirbJicn 

l\fen=27CB0 

SfclQy=274&1 



TcB 



■U5B0 



2-EBO 



26EB0 



3QEB0 



3SB0 



154 



Grocery Store Data 
Ra-226 

Set 4 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.CE3 



Forecast Total 
Frequency Chart 



175 Outliers 

1-451 




20BO 



23EBO 



27030 
rrren^H' 



3QEO 



34B0 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.70E+00 


Mode 


— 


Standard Deviation 


2.70E-01 


Variance 


7.28E-02 


Skewness 


0.02 


Kurtosis 


2.95 


Coeff. of Variability 


0.1 


Range Minimum 


1 .62E+00 


Range Maximum 


3.71 E+00 


Range Width 


2.10E+00 


Mean Std. Error 


1.91E-03 



155 



Grocery Store Data 
Ra-226 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



.029 
.021 
.014 

.07 
.ODD 



1.7EK) 



Overlay Chart 
Frequency Gbmpariscn 




21SB0 



26B0 



30EO 



EBaDdrihiicn 
Apte=52&1 

Baa=57S&1 
Stde=57tBO 



TcH 



33B0 



.QDB-T 
.001 

.an 

-031 
-OB 



Overlay Chart 
Frequency Dfference 



■ 


■ 


. -i. L. 1 1 1 


1 1 


r 1 


.IhLi 


L.i. . 


■■n 1 1 ■ 


'1 


1 ^ 


n'li || 


!■!■ "I 


■ 


■ 



EBaDaritilicn 
Afha=52»1 
ffia=57S&1 
Sde=57C&0 



TcH 



v&o 



219&0 



26B0 



30B0 



33B0 



156 



Grocery Store Data 
Ra-226 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



.as- 

.(21 • 

.ow ■ 

.007 
.GOO 



17EK) 



Overlay Chart 
Freqjency Comparison 




21SBO 



26EBO 



3QEB0 



Loqnorr^ Qslrbiai 

M3En=270&O 

StiDE*=2*&1 



TcH 



3SB0 



.004 

.002 

.000 

-02 

-CG4 



Overlay Chart 
Frequency Dfference 



uJ 



■■■■-■"""■"lllliTI 




UlUL 



krraiTEl Dsbrhiian 

l\ten=27C&0 

SUCEv=274&1 



Tea 



i7S*0 



21SB0 



262&0 



30BBO 



aso&o 



157 



Grocery Store Data 
Ra-226 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



17EB0 



Overlay Chart 
Frequency Comparison 




HBBO 



zffibK) 



30EBO 



Njnd DstritLtcn 

IVfean=27CBO 

3dC&/=27TjE1 



TcH 



33B0 



.C0B1 

.031 



.OD 
-C01 
-OB 



Overlay Chart 
Frequency Dfference 





■ 


I....JII ll 


. I.J.I 


1.. 1 . 


"'II 1 


'I 


1 •«'i|| 


1 J |l |i •! 


• 







NcttteI QsbitLticr) 

M=m=2XEtO 
StdDs/=27TjE1 



Tea 



1.7EBO 



21£*0 26EBO 3GE&0 3505*0 



158 



Grocery Store Data 
Ra-226 

Set 5 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
CE2 1 — 



Forecast: Total 
Frequency Chart 




A3 Outliers 
431 



3232 
2155 
1077 





15EB0 



23B0 



26EB0 
menses' 



3MB0 



33B0 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.70E+00 


Mode 


— 


Standard Deviation 


2.73E-01 


Variance 


7.47E-02 


Skewness 





Kurtosis 


2.95 


Coeff. of Variability 


0.1 


Range Minimum 


1.57E+00 


Range Maximum 


3.77E+00 


Range Width 


2.21 E+00 


Mean Std. Error 


1.93E-03 



159 



Grocery Store Data 
Ra-226 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



175BO 



Overlay Chart 
Frequency Comparison 




2-EBO 



263BO 



3QBB0 



ftBDdriliiicn 
A0b=48E&-1 
BBa=49?&1 
Stde=5«&0 



Toa 



3SB0 



002 

.GDI 

.ODD 

-£01 

-as. 



Overlay Chart 
Frequency Ofference 



■ 




■ 


,, 


IbLlh.i ,. 


Lid] 


1 II L. LI ■ i .■. 


■ "■|«|M, , || I -,| 


IT 


r^i 


II' | 


"* 1 1 1 I 1" 


!■■■■'! 1 | ' 



BBaDariWian 
AtfB=48E&-1 
Baa=49/&-1 
Sae=54E&0 



ToB 



1.7&0 2-EBO 2SB0 30E*O 39CEK3 



160 



Grocery Store Data 
Ra-226 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



.027 
.021 

.014 

.or 

.ODD 



17EB0 



Overlay Chart 
Frequency Comparison 




3GEB0 



Nfcrrrd DstribLBcri 

lfen=27C&0 

3dCB/=273&1 



TcB 



35030 



.002 1 




-002 



Overlay Chart 
Frequency Dff erence 







' 


lUlli.l i 


.lull 


. II. 1. II... 


■"■Tll'l |l 


n 


1 


"fl 


r f 




• 



Nrrrd Dstntuicn 

l\ten=27C&0 

9dQv=273&1 



Tea 



17EB0 



21EH5 



262BO 



30E&O 



3SB0 



161 



Grocery Store Data 
Ra-226 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



m 

(21 
.014 

m oop 

.000 



V7SBO 



Overlay Chart 
Frequency Comparison 




21SB0 



26B0 



30EBO 



itgoTfi DstribUicn 

IVban=27C&0 

SUQv=27E-1 



Tea 



35CBO 



.OOB 1 



.002 

.000 
-0C2 
-DOB 



Overlay Chart 
Frequency Dfference 













in. hl.i.liin 


"iHiimi'i « 


| ir t ■ 


■ 


' 



Lxrarrd DstribUicn 

Ntei=27C&0 

SUDa/=27E&1 



Tea 



IT&O 21EK) 2635K3 30E&O 350&O 



162 



Grocery Store Data 
Ra-226 

Set 6 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.022 1 — 



Forecast: Total 
Frequency Chart 



179 Cutlers 
-I-4B 




270BO 
nraTfyaEr 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.70E+00 


Mode 


— 


Standard Deviation 


2.72E-01 


Variance 


7.40E-02 


Skewness 


0.04 


Kurtosis 


3.03 


Coeff. of Variability 


0.1 


Range Minimum 


1.68E+00 


Range Maximum 


3.84E+00 


Range Width 


2.16E+00 


Mean Std. Error 


1.92E-03 



163 



Grocery Store Data 
Ra-226 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



m r 



.CED • 

.013 

.07 

.cm 



17EB0 



Overlay Chart 
Frequency Cbmparisai 




21EK) 



262BO 



30EBO 



B=taQanbtticn 
Afte=54&1 
Baa=68E&1 
Stcle=611B0 



Tea 



33B0 



.COBf 



GDI 

.GOD 
-0)1 
-OB 



Overlay Chart 
Frequency Difference 



. ■ I III _ ■!■- 1 II 



mV 



JL 



V 



■I J A I . . 



BEtaDsS-ihiicn 
Afte=54E&1 
B=la=68EB-1 
Sae=611&0 



Tea 



175B0 



21SB0 



262BO 



3CSB0 



35C&0 



164 



Grocery Store Data 
Ra-226 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



17&0 



Oreriay Chart 
Frequency Gbmpariscn 




219B0 



26B0 



303BO 



Njrrd Qstrtiiai 

IVfesn=27t&0 

SbCb/=27E1 



Tea 



33B0 



.OB 
.GC2 

.ODD 
-02 
-OB 



Overlay Chart 
Frequency Qfference 



■ hi i J. 
... ,i. ,i i,i i. in. 




■Jli.i -ill. ' 1 1 ■ _.« 



■ mi 



m 



r i • p ■ i 



Nfcnrd Dstrixdoi 

l\fen=27C&0 

StiCEv=275&1 



Tea 



17»0 21S&0 



2SB0 



30©o asc&o 



165 



Grocery Store Data 
Ra-226 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



.CGD 
.013 

.ay 
.an 



Overlay Chart 
Frequency Compar i so n 




kyoird DstrbJicn 

Wbm=27C&0 

SUDsv=27e&1 



TcB 



17SB0 



21EBO 



26B0 



3QE&0 



3SB0 



.QDB 

.GDI 
.COD 

-CD1 



Overlay Chart 

Frequency Dfference 



• 


1 




...Jl 


mil 


Lii 


i. .ij.iii.ii.ni.li 


■■■■■n-ii'i||i||||i|' ■ ■ r ic 


(i 






^F 


i 



Lxprmd Dstrbion 
IVfean=27CBO 

StlC&/=2^1 



TcB 



-OB 

17EK) 2-KBO 262BO 30©O 3SB0 



166 



Grocery Store Data 
Ra-226 

Set 7 

Crystal Ball Output 

Frequency Chart 



20,000 Tria"s 
CG3 1 



Forecast: Totd 
Frequency Chart 




235 Oilers 
— h 45D 




271B0 
nTsnfyear 



34B0 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.69E+00 


Mode 


— 


Standard Deviation 


2.71 E-01 


Variance 


7.36E-02 


Skewness 


0.3 


Kurtosis 


3.21 


Coeff. of Variability 


0.1 


Range Minimum 


1.66E+00 


Range Maximum 


4.11E+00 


Range Width 


2.45E+00 


Mean Std. Error 


1.92E-03 



167 



Grocery Store Data 
Ra-226 

Set 7 

Crystal Ball Output 

Distributions Fitting Chart 



.027 1 

.CEO 
.014 
.007 

.cm 



17E*0 



Overlay Chart 
Frequency Comparison 




21EK) 



262BO 



3CEBO 



G&TmaDslriiiiicn 
Ur=aC2&1 
SEde=38EE2 
3*pe=4SE&1 



Tea 



390&O 



COB 




-£CB 



Overlay Chart 
Frequency Dffererce 



■ 




■ 


..!.. .1.1 ill 


ii i 


i 


1 .l.ll l.l.ii.. ... 


■■ 'i "" I'l ' Mil ■ r 


| ''il'l'i il 1 " t 


■ 


■ 



GferrrraDstritiiicn 
lrc=aCE&1 
Sc=le=38E&2 
ShipB"48BB'1 



Tea 



17EB0 



21&0 



26&0 



3QE&0 



3SBO 



168 



Grocery Store Data 
Ra-226 

Set 7 

Crystal Ball Output 

Distributions Fitting Chart 



.(27 1 

.CED 

.014 

.C07 

.an 



1.7EE+0 



Overlay Chart 
Frequency Comparison 




2-GE*0 



26BO 



aa&o 



NjtteI DstrittScn 

M3m=27CBO 

3dQy=271&1 



Tdd 



3SB0 



.ow 

.02 

QCD 

-CC2 

-DM 



Overlay Chart 
Frequency Dff erence 



■ 






. ..II.I. Ill.l.ll.l 


..II.I 


illllli 


i.,lii„, 


PTPI 


WT 


jr i i||ii»-||M 


■ 


1 1 



NkrrrEl Dslribiicri 
l\ten=270&0 

3riCEv=271&1 



TcB 



175*0 



21&0 



26B0 



aoa&o 



2SB0 



169 



Grocery Store Data 
Ra-226 

Set 7 

Crystal Ball Output 

Distributions Fitting Chart 



.027 

.014 
.007 
ODD 



17EK) 



Overlay Chart 
Frequency Comparison 




2«BO 



263BO 



3QEBO 



LqgroTTBl Ddrtaicn 

Wfean=27t&0 

SUC6/=27I&1 



Tea 



asc&o 



.OB 

.GDI 

QD 

-GDI 

-COB 



Overlay Chart 
Frequency Dfference 



• 




■ 


... 1. .I.J ill 


ii_I.I_ 


. i.l i 1 Mi 1 1 ii ..... 


■' H IP l|'l |||> 


1 1 ■up h' w 


■ 





L uj uii d Oslrhiiai 
M=m=27C&0 

SbQy=271E-1 



TcB 



17EBO 



2-BBO 



262&0 



3GEB0 



33&0 



170 



Grocery Store Data 
Ra-226 

Set 8 

Crystal Ball Output 

Frequency Chart 



20,000 Trids 
.023 



forecast: Total 
Frequency Chart 



-B6 Outliers 
— r- 462 




Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


2.70E+00 


Median 


2.70E+00 


Mode 


— 


Standard Deviation 


2.72E-01 


Variance 


7.38E-02 


Skewness 


-0.01 


Kurtosis 


3.02 


Coeff. of Variability 


0.1 


Range Minimum 


1.70E+00 


Range Maximum 


3.79E+00 


Range Width 


2.09E+00 


Mean Std. Error 


1.92E-03 



171 



Grocery Store Data 
Ra-226 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



17EB0 



Cverlay Chart 
Frequency Comparison 




21SB0 



2ffiB0 



3G6BO 



BaaDsb-itUion 
Affta=4SC&-1 
EBa=49EH 
SC=le=541B0 



TcB 



33B0 



.CEB-r 

.era 

COD 
-DD1 
-OB 



Overlay Chart 
Frequency Dfference 





■ 


....III 


ill ...1. .. 


hi 


1 i.i nil ..i ... 


■ |ii|i n | i 


'' 1 


i[ - . 




■ 



BaaDSriWcn 
Af*B=49C&1 
Baa=4£E&1 
Sde=541B0 



TcH 



1.7EK) 



2-H&0 



262BO 



30EK) 



3SB0 



172 



Grocery Store Data 
Ra-226 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



.CBB 
.021 

.014 
.07 
.ODD 



1.75BO 



Overly Chart 
Frequency Comparison 




21EO 



263BO 



30SO 



NjrnJ Dstrixtcn 

l\*an=27TJ&0 

SfciQy=272&1 



Tea 



33B0 



.com 



.0D1 

.ODD 

-fJOl 

-fXB 



CVerlay Chart 
Frequency Dfference 



• 




. 1. . .ll .1 1 


ill 


Jillll III. 


... 1 1 1 .il. i i... 


■■■ >l>llll'lll pi 


1 




T 


r 


'i 


in" i M 


• 







ttarrsl DstrbJjcn 

l\ten=27Tj&0 

ajQv=27Z-1 



Tea 



17S0 21SB0 26B0 



30&O 3SB0 



173 



Grocery Store Data 
Ra-226 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



.CBB 
.021 
.014 
.07 
ODD 



Overlay Chart 
Frequency Comparison 




Lyunti DstritUicn 

IVter=27rj&0 

aiDB/=27E&1 



TdEl 



U8B0 21&0 263&0 30EBO 3S&0 



0D3 

0Q2 

ODD 

-C02 

-CCB 



Overlay Chart 
Frequency Dfference 



=^"1 



r 



jiuikuk 



Lojund Dstritiijcn 

IVban=27rj&0 

SbC&/=27«-1 



Tea 



1.7S&0 21&0 2SBO 30SO 



35B0 



174 



Grocery Store Data 
Ra-226 

Set 9 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.06 



Forecast: Total 
Frequency Chart 




3)9 Outliers 

92 



lliiHUiiiini fn 




73E-2 



48S0 



95B0 
rtTan^ea' 



1.4&1 



1.91B-1 



Forecast: Total 




Statistic 


Value 


Trials 


20000 


Mean 


4.39E+00 


Median 


2.71 E+00 


Mode 


— 


Standard Deviation 


5.62E+00 


Variance 


3.16E+01 


Skewness 


5.6 


Kurtosis 


69.91 


Coeff. of Variability 


1.28 


Range Minimum 


7.33E-02 


Range Maximum 


1.50E+02 


Range Width 


1.50E+02 


Mean Std. Error 


3.98E-02 



175 



Grocery Store Data 
Ra-226 

Set 9 

Crystal Ball Output 

Distributions Fitting Chart 



QQC&O 



Overlay Chart 
Frequency Comparison 




5CIB0 



ICDEH 



1.3&1 



LrgrorrrEl DslrfcUicn 

l\tei=43EB0 

SbCB/=52B0 



Tea 



20CB-1 



.003 1 




-CCB 



T 



Overlay Chart 
Frequency Dff erence 



WWjlW JA **rV»^i 



Fmi 



IxyuniJ DstrbJiai 

M=m=43E&0 

SUC&/=55B0 



TcB 



QOCBO 50CBO 10D&1 



1.3B-1 



2C0&-1 



176 



Grocery Store Data 
Pb-210 

Setl 

Crystal Ball Output 

Frequency Chart 



20,000 Trids 
.023 



Forecast: Total 
Frequency Chart 




28 Outliers 

4E3 



327 
2255 
1132 





677B2 



Forecast: Total 




Statistic Value 


Trials 


20000 


Mean 


5.18E+02 


Median 


5.14E+02 


Mode 




Standard Deviation 


6.41 E+01 


Variance 


4.10E+03 


Skewness 


0.41 


Kurtosis 


3.26 


Coeff. of Variability 


0.12 


Range Minimum 


3.09E+02 


Range Maximum 


8.72E+02 


Range Width 


5.63E+02 


Mean Std. Error 


4.53E-01 



177 



Grocery Store Data 
Pb-210 

Setl 

Crystal Ball Output 

Distributions Fitting Chart 



3SB2 



Overlay Chart 
Frequency Comparison 




43&2 



525B2 



612B2 



kgrcmnd DslrhJicn 
SbCe/=63&1 



Tea 



7.CE&2 



.002 1 




-02 



Overlay Chart 
Frequency Dff erence 









■ 


. 1 .hill .1 1 J .. 


.lit,, 


Ujj 


.J L.I .. 


r i ^rr 


| ||l 1 "|T| 


■ 





liyuiid Dstrbicn 

Mhi=51£B2 

StlCB/=63E&1 



TcH 



3SB2 



43EB2 



52E&2 



613&2 



7.G0&2 



178 



Grocery Store Data 
Pb-210 

Set 2 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.022 



forecast: Total 
Frequency Chart 




S3 Outliers 

48 



El 

I 



i» 



521&2 
nTer/yer 



Forecast: Total 




Statistic Value 


Trials 


20000 


Mean 


5.18E+02 


Median 


5.14E+02 


Mode — 




Standard Deviation 


6.46E+01 


Variance 


4.18E+03 


Skewness 


0.36 


Kurtosis 


3.19 


Coeff. of Variability 


0.12 


Range Minimum 


3.13E+02 


Range Maximum 


8.43E+02 


Range Width 


5.29E+02 


Mean Std. Error 


4.57E-01 



179 



Grocery Store Data 
Pb-210 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



30B-2 



Overlay Chart 
Frequency Comparison 




4QC&2 



CfcrrraDstritiiicn 
Le = 1.57B2 
SbEle=1.15EH 
&Bpe=311EH 



Tea 



70B2 



ODB 1 




-OB 



CVerlay Chart 
Frequency Dffererce 



■ ■■. ■ '■ M>A 



h 



a 



w 



IW 1 ^ 



QnrraDstritiliai 
loc=1SB2 
Sde=1.15EH 
9^e=311B-1 



Tea 



30B2 



40C&2 



50B2 



6QDB2 



7CT&2 



180 



Grocery Store Data 
Pb-210 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



m 

.CEO 
.013 
.007 

.ox 



3CCB2 



Overlay Chart 
Frequency Ctmpari son 




40CB-2 



5CC&2 



60DB2 



Nxnd Dstrihiicn 

l\ten=51E&2 

SdCB/=64c&-1 



Tea 



7CC&2 



.0C5 




-02 



Owerlay Chart 
Frequency Dfference 



■ 






• 


Lllllllljllll . -Il-ll 


J, 


ill 


Ll-ll . 


■W 


w 


1 1 i|| ||i| 1 »| 1 


I 


I 



Nmrd Dstribicn 

Nten=51S&2 

3dQy=64EH 



Tea 



3CC&2 40CB2 5CC&2 6CCB2 7CC&2 



181 



Grocery Store Data 
Pb-210 

Set 2 

Crystal Ball Output 

Distributions Fitting Chart 



m 

.013 

.07 

ODD 



3CC&2 



CVerlay Chart 
Frequency Comparison 




40092 



6GC&2 



Lxjund Dstritiijai 

Nten=51£&2 

StJD&/=64?&1 



TcH 



7.CC&2 



.003 

.001 

.ODD 

-001 

-ODB 



Overlay Chart 
Frequency Dfference 



■ 




■ 


... ll, .11 III III, 




.ll 1 iLi 


1 "1 III - 1 1 1 ■ " 


II '"1 •II ipll'l" ■■ 





LyuiitJ Daribdicn 

l\fen=51£B2 

SUC&/=6<fiB-1 



Tea 



30C&2 



400B2 



50032 



60C&2 



7.CCB2 



182 



Grocery Store Data 
Pb-210 

Set 3 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
022 1 — 



Fbrecast: Total 
Frequency Chart 



£5 Outliers 

436 




Forecast: Total 




Statistic Value 


Trials 


20000 


Mean 


5.18E+02 


Median 


5.14E+02 


Mode — 




Standard Deviation 


6.42E+01 


Variance 


4.13E+03 


Skewness 


0.37 


Kurtosis 


3.23 


Coeff. of Variability 


0.12 


Range Minimum 


3.12E+02 


Range Maximum 


8.53E+02 


Range Width 


5.41 E+02 


Mean Std. Error 


4.54E-01 



183 



Grocery Store Data 
Pb-210 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



3SB2 



Overlay Chart 
Frequency Comparison 




43EB2 



52»2 



6-CB2 



C^rma Dslriliticn 

im=i.e&2 

Sae=1.16&1 
3^3e=3CE&1 



Tea 



70B-2 



.02 
.001 
.ODD 

-mi 

-DQ2 



Overlay Chart 
Frequency Dffererce 



.1, ..l.i.ij 



mn 



lil 



__■! Ij I II . » ■ 



G&rmaQslrihlJcri 
L3C=1.9&2 
Sae=1.16B-1 
3^e=3CEB-1 



Tea 



3S&2 



43&2 



52&2 



6t&2 



7.0&2 



184 



Grocery Store Data 
Pb-210 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



.CE3 
.017 
.011 
.006 
.000 



33B-2 



O/erlay Chart 
Frequency Ctmparison 



jiilAiilrr 


jfll iiiN 


JUlHIUIIHUliUlfflllHIiriihh 


^JMi M 1 ll 1 lliliw 



43E+2 



52»2 



613B-2 



Nfcrrrti QSritUJcn 

lfei=51£&2 

StiQy=642B-1 



Tea 



7.CT&2 



0C4 

.002 

.000 

-032 

-0C4 



CVerlay Chart 
Frequency Dffererce 



III 


■ 


ii.ii.in.ij.. I i. iii lliil 


L.iliii. . 


rni 


iji'i ■ 1 1 iiii i ■■■■-■■ 


I 


■ 



Nbnrrt Ddritiijari 

Nten=51fi&2 

SfcJCEv=64&1 



Tea 



33&2 



43EB2 



52&2 



613B-2 



70&2 



185 



Grocery Store Data 
Pb-210 

Set 3 

Crystal Ball Output 

Distributions Fitting Chart 



35C&2 



Overlay Chart 
Frequency Comparison 




43EB2 



52E2 



6t&2 



l£gmm=l nslrtiiian 

Mhi=518B2 

SUDb/=643B-1 



TcH 



7.CC&2 



.02 

.GDI 

.000 

-J0O1 

-02 



Overlay Chart 
Frequency Off erence 



AA 



aA 



rn 



I ill. 



..Hi h I I.I ll.i 

H r Mi I 1 W 



LcgnorrrEl DslrfcUicn 

Htei=518&2 

SUCB/=64B-1 



TcB 



3S&2 



43EB2 



52E&2 



6t&2 



7.0C&2 



186 



Grocery Store Data 
Pb-210 

Set 4 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 

.023 



.017' 
.011 
.003 
ODD 



ih.iiilll 



Forecast: Total 
Frequency Chart 



■60 Cutlers 
453 



3S&2 




Forecast: Total 




Statistic Value 


Trials 


20000 


Mean 


5.18E+02 


Median 


5.16E+02 


Mode 




Standard Deviation 


6.47E+01 


Variance 


4.18E+03 


Skewness 


0.2 


Kurtosis 


3.08 


Coeff. of Variability 


0.12 


Range Minimum 


2.82E+02 


Range Maximum 


8.70E+02 


Range Width 


5.88E+02 


Mean Std. Error 


4.57E-01 



187 



Grocery Store Data 
Pb-210 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



.CBD 
.013 
.007 
.ODD 



30CE+2 



Overt*/ Chart 
Frequency Cbmparison 



jjj| iJjjKi 


■ 


jdjl ||[|K 


i- 


>jjjj 


IllhnTTTTi 



4CC&2 



50E+-2 



6QC&2 



GErrrraDslrihicn 
Le,=-12&2 
Stde=647BO 
3TEpe=9SEEH 



TcB 



7.Q&2 



.02 
.GDI 

.ODD 
-031 
-02 



Overlay Chart 
Frequency Dfference 







■ 


1. .Ill Jill 1 


ni 


lh 1 1 III i . . i..l L .. 


- ■ M f f || II' I ■ 'III ■ i 


r 


'i n| >i|i ■ 


! 




■ 



G&nTaDstriiiiJcn 

lffi=-12SB2 

Stcle=647B0 

3^b=99E&1 



Tea 



30B2 40032 50CB2 6CEB2 7.0032 



Grocery Store Data 
Pb-210 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



.(27 1 

.CBD 

.013 

.007 

.ODD 



3CC&-2 



Overlay Chart 

Frequency Cbmpari son 




4CC&2 



5CD&2 



60C&2 



Ntrrrd Dsbritiiicn 

Mhi=51E&2 

SfciD3/=64/B-1 



Tea 



7.0CEf2 



XDB1 




-03 



O/erlay Chart 
Frequency DfFererce 



. I 


1 


i.i.i. illlil- 1 L in hi 1 


ll.lil.. il.ii 


'l'| 


ill 


1 


| '|H 1 1 1 —i 








• 



Nmnd DstritUicn 
IVfem=51SB-2 

SHD=v=64&1 



TaB 



30B-2 



4CT&2 



50CB2 



6CTB2 



7.GCB2 



189 



Grocery Store Data 
Pb-210 

Set 4 

Crystal Ball Output 

Distributions Fitting Chart 



.027- 

.cm 

.013 
.007 
COO 



30B2 



O/erlay Chart 
Frequency Comparison 




4CT&2 



50C&2 



60B2 



LyuiittDslrtUJcn 

Mar=51E&2 

StlCfv=65&1 



Tea 



7.CC&2 



.003 f 



.002 

.ODD 
-CC2 
-OB 



Overlay Chart 
Frequency Dfference 



,. ■ hi j. 

- •-■■i|i— i |jr| 



llJlillu. i lUl. 

||'|| I'j ■ T 



pr 



Lqjrrmd DslrhJicri 
l\tei=51EB2 

SbCB/=65&1 



TcH 



3CCB2 40C&2 5C0&2 60CE+2 



7.QC&-2 



190 



Grocery Store Data 
Pb-210 

Set 5 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.022 



.016 



.011 



.CD5 



.ODD 



•uiimii 



Forecast: Total 
Frequency Chart 



237CU)iers 
433 



357B2 




Forecast: Total 






Statistic 


Value 




Trials 




20000 


Mean 




5.18E+02 


Median 




5.16E+02 


Mode 


— 




Standard Deviation 




6.39E+01 


Variance 




4.09E+03 


Skewness 




0.21 


Kurtosis 




3.12 


Coeff. of Variability 




0.12 


Range Minimum 




3.02E+02 


Range Maximum 




8.43E+02 


Range Width 




5.41 E+02 


Mean Std. Error 




4.52E-01 



191 



Grocery Store Data 
Pb-210 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



33B2 



Overlay Chart 
Frequency Cbmparison 




GfrmBDslritiiian 

Lcc=-1.1£t2 

Sae=64B0 



Tea 



43&2 



52&2 



613B-2 



7GDB2 



.02 

.001 

.ODD 

-£D1 

-02 



Overlay Chart 
Frequency Dffererce 



• 




■ 


..J Jl Jill 


, 


,ll .1,1. J 


,1.1 .i. 


"in ip | || ||'n| 


r |ri| ■ 


n ii 


IP i- i"-"i|'-i 









QnTTBDslriliticn 
lffl=-fHB2 

Stde=64B0 

3^e=99fB-1 



Tea 



3S&2 



43&2 



52»2 



612B2 



7.0&2 



192 



Grocery Store Data 
Pb-210 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



Overlay Chart 
Frequency Comparison 




3SB-2 



43»2 



52&2 



6t&2 



Nfcrrrt Daribdicn 

ltei=5ia&2 

8dDB/=63EEH 



Tea 



7QDB-2 



.003 

0D1 

CCD 

-JDD1 

-OB 



Overlay Chart 
Frequency Dfference 



• 




■ 


JJ.il .III i .1 


J 


,in 


JU 


Jill J . 


■ |. -. 




1" 


II 1 IP ll.llll-ll- 




1 1 


■ 



Nrmd Dsb-ibiiGn 
Mhi=51S&2 



Tea 



193 



Grocery Store Data 
Pb-210 

Set 5 

Crystal Ball Output 

Distributions Fitting Chart 



33B-2 



O/erlay Chart 
Frequency Comparison 




6T&2 



LyuntJ Dstrbiicn 

l\feri=51E&-2 

SUDev=646EH 



Td3l 



7.0CB2 



.003 1 




-OB 



Overlay Chart 
Frequency Off erence 



■ 


• 


.II ,lll 


iJuL 


...,i. . I uLi.i.1... 


l'lllll'IIH jl ■ ■ 


1 PI 11 ! 1 


Hi" i- 


■ 


■ 



Injund Dsfrhiian 

l\*m=518E+2 

StlCB/=&€B-1 



TcB 



33B2 



43E&2 



525B2 



613B2 



7.0C&2 



194 



Grocery Store Data 
Pb-210 

Set 6 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.022 



Forecast: Total 
Frequency Chart 




210 Outliers 
T 434 



3255 

217 

KB5 





67&2 



Forecast: Total 




Statistic Value 


Trials 


20000 


Mean 


5.17E+02 


Median 


5.14E+02 


Mode — 




Standard Deviation 


6.38E+01 


Variance 


4.07E+03 


Skewness 


0.22 


Kurtosis 


3.14 


Coeff. of Variability 


0.12 


Range Minimum 


2.69E+02 


Range Maximum 


8.45E+02 


Range Width 


5.76E+02 


Mean Std. Error 


4.51 E-01 



195 



Grocery Store Data 
Pb-210 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



3S&2 



Overlay Chart 
Frequency Comparison 




43&2 



52&2 



6t&2 



C^rmaDstritUlcn 

Lr.=-79B-1 

Sae=68EB0 

9^e=a6E&1 



Tea 



7CCB2 



.GD3 1 




O/erlay Chart 
Frequency Dffererce 



-OB 



■ 


..i Lull ill J III. ,il 1 1 hi i .......I. . 


. I' "M | | " 


• i ■ 1 1' jipni I.- ■ 


• 


■ 



GbTrraDstritilicn 
lo:=-7.aB-1 
Sde=686BO 
9q£=86EH 



Tea 



33B2 43&2 52SB2 613B2 7.0B2 



196 



Grocery Store Data 
Pb-210 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



3SB2 



Overlay Chart 
Frequency Comparison 




43&2 



52&2 



6-G&2 



Nbml DdriWicn 

Nfem=517&2 

adDB/=63E&1 



Tcfei 



7.GC&2 



QDB 

.GDI 

.ODD 

-001 

-OB 



Overlay Chart 
Frequency Dfference 



■ 


■ 


..hi ill 1 1 , 1 


. I 1 1 1. ill. i i i 


'■ m "ff nrif 


|i> r i I'pii |i«"'i 




■ 



t^trrrd QstritxEan 

l\*ai=517&2 

atCB/=63&1 



TcfcJ 



39B2 43EB2 52&2 



613&2 7.0C&2 



197 



Grocery Store Data 
Pb-210 

Set 6 

Crystal Ball Output 

Distributions Fitting Chart 



3SB-2 



Overlay Chart 
Frequency Campari son 



43EB-2 




6t&2 



Lxpjrrcl Dslrbicn 
Htei=517&2 



TcB 



7.0&2 



.OB 

.001 

.ODD 

-DD1 

-az 



Overlay Chart 
Frequency Qfference 











III J 


1 .IL ..1 ■ i 1 illlll.iil. 


■■ ■■" "Jll " "1 1'l »" M ' 1 


'I 


II ll'l'l'" ' 


• 







ky untJ DdrhJicn 
Nten=517B2 

adDa/=64&1 



TcB 



3SB2 



43EB2 



52&2 



612&2 



7.CC&2 



198 



Grocery Store Data 
Pb-210 

Set 7 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.CE3 



.017 
.011 
.006 
.ODD 



Forecast: Total 
Frequency Chart 



221 Outliers 

HS9 




35EB-2 



43B&2 



521&2 
rrr&rtyB 



6CE&2 



68EB2 



Forecast: Total 




Statistic Value 


Trials 


20000 


Mean 


5.18E+02 


Median 


5.14E+02 


Mode — 




Standard Deviation 


6.47E+01 


Variance 


4.18E+03 


Skewness 


0.39 


Kurtosis 


3.26 


Coeff. of Variability 


0.12 


Range Minimum 


3.04E+02 


Range Maximum 


8.33E+02 


Range Width 


5.29E+02 


Mean Std. Error 


4.57E-01 



199 



Grocery Store Data 
Pb-210 

Set 7 

Crystal Ball Output 

Distributions Fitting Chart 



.(EM 



.GED 


£ 


-■ 


m 


= .013 


E 


— 


i 


SI .007 


"™ 


.000 



3CCB2 



Overlay Chart 
Frequency Comparison 




40CB-2 



50CB2 



60CB2 



Lcgrcrrrd Dslrbicn 

Nban=51EB2 

SUCB/=64B&1 



TcH 



7.0C&2 



.002 T 



.001 

.000 

-fJDl 



Overlay Chart 
Frequency Dff ererce 



.. .1.11,1, „i..„i,i„ 

I'M ||l||| 



JllJ 



PT[ 



I 



ilj J... i j ■- 



» in ■■■ i 



pir 



LcgxnTEl DstrbJcn 
lvfen=518&2 

StlCEv=646&1 



Tea 



-J002 I r 

3CC&2 400&2 500B-2 600B2 7.0C&2 



200 



Grocery Store Data 
Pb-210 

Set 8 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
.023 1 — 



Forecast: Total 
Frequency Chart 




Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
5.18E+02 
5.16E+02 

6.37E+01 

4.06E+03 

0.21 

3.16 

0.12 

2.75E+02 

8.04E+02 

5.29E+02 

4.50E-01 



201 



Grocery Store Data 
Pb-210 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



39CB2 



Overlay Chart 

Frequency Cbmpari son 




43EB2 



529=f2 



613B-2 



GfrmaDslribiJcn 

loc=-1.1£B2 

Sde=637&0 

S^£=9SC©-1 



Toa 



7.CE&2 



.002 1 



.cm 

.OD 

-mi 

-J0C2 



Overlay Chart 
Frequency Dffererce 





■ 


•ilLiI.ii 


lL. , 


^J. IjJ 


.1.1 1 i - 


i" -| |" i| '|'||ii | 


| | 'III' l|l|-ill"« 




■ 



GSTmaQstritiiicn 

Lr=-1.1&2 

Stde=637BO 



TcB 



33B2 



43&2 



52»2 



6t&2 



7CC&2 



202 



Grocery Store Data 
Pb-210 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



3SB2 



CVerlay Chart 
Frequency Comparison 




43E&2 



52EB2 



613&2 



Nrmd DstribUicn 
l\*ai=518B2 

adCB/=63&1 



Tea 



7GCB-2 



.003 



-OB 



Overlay Chart 

Frequency Dfference 




TPfT 



M 




Tn"nr 



mnr 



htnrt Dstritita 

Msn=5ie&2 

3dQy=637B-1 



ToB 



3S&2 43&2 52Et2 613&2 



70C&2 



203 



Grocery Store Data 
Pb-210 

Set 8 

Crystal Ball Output 

Distributions Fitting Chart 



3SB2 



Overlay Chart 
Frequency Comparison 




43E&2 



52»2 



6t&2 



IxguniJ DstrbJicn 
Wfem=518fr2 

SbD=v=64&1 



Tea 



7.GC&-2 



.003 

.GDI 

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204 



Grocery Store Data 
Pb-210 

Set 9 

Crystal Ball Output 

Frequency Chart 



20,000 Trials 
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Forecast: Total 
Frequency Chart 




SD2 Outliers 
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Forecast: Total 

Statistic 

Trials 

Mean 

Median 

Mode 

Standard Deviation 

Variance 

Skewness 

Kurtosis 

Coeff. of Variability 

Range Minimum 

Range Maximum 

Range Width 

Mean Std. Error 



Value 



20000 
8.44E+02 
5.25E+02 

1.08E+03 

1.16E+06 

6.02 

86.32 

1.27 

1.00E+01 

3.15E+04 

3.15E+04 

7.61 E+00 



205 



Grocery Store Data 
Pb-210 

Set 9 

Crystal Ball Output 

Distributions Fitting Chart 



QQGBO 



Overlay Chart 
Frequency Comparison 




1.0CB3 



20E+-3 



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K 


^ 


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i 


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REFERENCES 



Argonne National Laboratories (ANL) (1989). Residual Radiation Dose Contamination 
Program-RESRAD . http://web.ead.anl.gov/resrad. 

Birky, B. (1990). Dose Assessment From Radioactivity in Foods Grown on Mined 
Florida Phosphate Lands . Master's thesis, University of Florida, Gainesville, FL. 

Borrud, L., Enns, C. W., & Mickle, S. 1996. What We Eat in America: USDA Surveys 
Food Consumption Changes. Food Review 14-15 

Burk, R. J., Jr. (2000). Risk Assessment: Position Statement of the Health Physics 
Society . McLean, VA: Health Physics Society. 

Carvalho, F. P. (1995). 210 Polonium and 210 Lead Intake by the Portuguese 

Population: The Contribution of Seafood in the Dietary Intake of 210 Polonium 
and 210 Lead. Health Physics 69(4): 469-480. 

Decisioneering. (1996). Crystal Ball 4.0 User Manual . Denver, CO: Author. 

Enns, C. W., Goldman, J. D., & Cook, A. (1997). Trends in food and nutrient intakes by 
adults: NFCS 1977-78, CSFII 19889-91, and CSFII 1994-95. Family Economics 
and Nutrition Review 10(4): 1-15. 

Environmental Protection Agency. (1988). Limiting Values of Radionuclide Intake and 
Air Concentration and Dose Conversion Factors for Inhalation. Submersion, and 
Ingestion . Oak Ridge, TN, Oak Ridge National Laboratory. 

Environmental Protection Agency. (1995). Cancer Risk Coefficients for Environmental 
Exposure to Radionuclides: Federal Guidance Report No. 13 . (Document 402-R9- 
9001). Washington, DC: Author. 

Environmental Protection Agency. (1997). Exposure Factors Handbook. Vol. H-Food 
Ingestion Factors (Document 600/P-95/002Fa). Washington, DC: Author. 

Guidry, J. J., Bolch, W. E., Roessler, C. E., McClave, J. T., & Moon, J. R. (1986). 
Radioactivity in Foods Grown on Florida Phosphate Lands . Bartow, FL, Florida 
Institute of Phosphate Research. 



206 



207 



Guidry, J. J., Roessler, C. E., Bolch, W. E., McClave, J. T., Hewitt, C. C, & Abel, T. E. 
(1990). Radioactivity in Foods Grown on Mined Phosphate Lands . Bartow, FL, 
Florida Institute of Phosphate Research. 

Harley, J. W. (1988). Naturally occurring sources of radioactive contamination. In J. H. 
Harley, G. D. Schmidt, and G. Silini (Eds.), Radionuclides in the Food Chain (pp. 
58-71). New York: Springer-Verlag. 

International Council on Radiation Protection (1994). Dose Coefficients for Intakes of 
Radionuclides by Workers. Annals of the ICRP 24(4): 1-83. 

International Council on Radiation Protection (1996). Age-dependent Doses to 
Members of the Public from Intake of Radionuclides: Part 5 Compilation of 
Ingestion and Inhalation Dose Coefficients. Annals of the ICRP 26(1): 1-89. 

Linsalata, P. (1994). Uranium and Thorium Decay Series Radionuclides in Himan and 
Animal Foodchaines~A Review. Journal of Environmental Quality 23: 633-642. 

Morse, R. S. & Welford, G. A. (1971). Dietary Intake of 210Pb. Health Physics 21: 53- 

55. 

Nuclear Regulatory Commission (1977). Regulatory Guide 1.109: Calculation of 

Annual Doses to Man from Routine Releases of Reactor Effluents for the Purpose 
of Evaluating Compliance with 10 CFR Part 50, Appendix I. Regulatory Guide 
1.109 . Washington, DC: Author. 

Nuclear Regulatory Commission (2000). NRC Mission . May 11, 2000. 
www.NRC.gov. 

Pennington, J. A. T. (1983). Revision of the Total Diet Study, Food List and Diets. 
Journal of the American Dietetic Association 82f2): 166-173. 

Pennington, J. A. T. (1992). Total Diet Studies: The 1990 Revision of the FDA Total 
Diet Study. Journal of Nutritional Education 24(4): 173-178. 

Pritchard, P. C. H., & Bloodwell, J. M. (1985). Multidisciplinarv Study of 

Radionuclides and Heavy Metal Concentrations in Wildlife on Phosphate Mined 
and Reclaimed Lands . Maitland, FL, Audubon Society. 

Shleien, B., Slaback, L. A., Jr., & Birky, B. K. (1998). Handbook of Health Phvsics and 
Radiological Health . Baltimore, MD: Williams and Wilkins. 

Turner, J. E., Bogard, J. S., Hunt, J. B., & Rhea, T. A. (1988). Problems and Solutions 
in Radiation Protection. Elmsford, NY: Pergamon Press. 



208 



U.S. Department of Agriculture (USDA). (1996). Continuing Food Survey of Intake by 
Individuals II. (http://www.barc.usda.gov/bhnrc/foodsurvey/cfsii94.html). 

U.S. Department of Commerce. (1983). Radiological Assessment: A Textbook on 
Environmental Dose Analysis : Oak Ridge, TN, NTIS. 

Weiner, E. R. (2000). Applications of Environmental Chemistry . Boca Raton, FL: 
Lewis Publishers. 

Yu, K. N., & Mao, S. Y. (1999). Assessment of Radionuclide Contents in Food in Hong 
Kong. Health Physics 77(6): 686-696. 



BIOGRAPHICAL SKETCH 

Ward L. Dougherty was bom in Stamford, Connecticut, on February 27, 1963. 
He was raised in Lutz, Florida. He joined the Navy in December 1986. He met and 
married his wife, Gwendolyn Bennett, while in the Navy on August 18, 1990. His son, 
Justin, was bom while he was stationed in Charleston, South Carolina, on August 24, 
1991. His daughter, Michelle, was bom just prior to completing his Naval service on 
February 5, 1993. He served on board two submarines, the U.S.S. James Madison (SSBN 
627) and the U.S.S. Dolphin (AGSS 555). He achieved the engineering watch supervisor 
and engineering duty petty office qualification while on board the Madison. As an E-5 he 
was one of only two people to ever qualify, in the 30-year history of the boat, to that 
watchstation at his rank. His awards include Humanitarian, Good Conduct (2), Sea 
Service Ribbon, National Defense Service Medal, and the Submarine Qualification 
with four patrol pins. He completed over six years with ah honorable discharge in March 
1993. 

He attended the University of Florida, College of Engineering, Department of 
Nuclear and Radiological Engineering, from April 1993 until May 1999. He worked for 
Innovative Nuclear Space Power and Propulsion Institute from 1996-1999 and has 
attended numerous space nuclear power conferences. He graduated from nuclear 
engineering with a bachelor's degree with high honors in August 1996 and with a master's 
degree in December 1999. He transferred to environmental engineering and subsequently 



209 



210 



dual enrolled in nuclear and environmental to pursue concurrent Ph.D. degrees in nuclear 
engineering and environmental engineering. 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




W. Emmett Bolch, Jr., Chair 

Professor of Environmental Engineering Sciences 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



Wesley E. Bol£h 



Wesley 

Associate Professor of Nuclear and Radiological 
Engineering 



I certify' that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



fate- 



William S. Properzio i. 

Associate Professor of Environmental Engineering 
Sciences 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 

U n : f 



G. Ronald Dalton 

Professor of Nuclear and Radiological Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




Jtt<~ -*?• >^w 



Angela/S. Lindner 
Assistant Professor of Environmental Engineering 
Sciences 



This dissertation was submitted to the Graduate Faculty of the College of 
Engineering and to the Graduate School and was accepted as partial fulfillment of the 
requirements for the degree of Doctor of Philosophy 



May 2001 



/ 




M. 73ck Ohanian 

Dean, College of Engineering 



Winfred M. Phillips 
Dean, Graduate School 









Lb 

7bo\ 



UNIVERSITY OF FLORIDA 



3 1262 08555 1751